I will present the results of a Monte Carlo simulation of a planar accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole. The gas is assumed to be in thermal equilibrium at infinity, where it obeys the Maxwell-Jüttner distribution. This simulation methodology builds on the approach developed last year for a stationary Schwarzschild black hole. I will elucidate the modifications necessary for setting up the simulation for the complexities introduced by black hole motion. Furthermore, our Monte Carlo results consistently confirm the analytically derived exact expressions for particle current density in all examined cases.

By considering the dynamics of spectrally concentrated wave-packets propagating in media with a slowly-varying periodic structure, we rigorously derive a novel dynamical system for the evolution of observables associated to the wave, specifically its center of mass and momentum. The system corrects the standard result relating wave-packet velocity to the derivative of the dispersion band. The corrections include an anomalous velocity due to Berry curvature and an interesting "particle-field coupling'' effect where the evolution of the observables, which are discrete degrees of freedom, becomes coupled to the evolution of the wave-packet envelope, a continuous degree of freedom. Although our derivation focuses on the case of waves described by the linear Schrödinger equation, we expect that the derivation can be carried out for other linear PDE describing waves.

This talk concerns the problems of energy concentration and structure formation in Hamiltonian systems. I will present a novel mechanism for the dynamical formation of condensates, which markedly differs from that predicted by the wave turbulence theory. I will also show that the process is accompanied by a deterministic turbulent cascade that concentrates energy at arbitrarily small scales in finite time. The result is fully analytic, based on explicit solutions representing all the aforementioned phenomena. This talk is based on my recent work: Phys. Rev. E 110, 034107 (2024).

That light propagating in a gravitational field gets frequency-shifted is one of the basic consequences of any metric theory of gravity rooted in the equivalence principle. At the same time, also a time dependent material's refractive index can frequency-shift light propagating in it. The mathematical analogy between the two effects is such that the latter has been used to study the optical analogue of a black-hole spacetime. In the work that I will present [1], we combine these two effects by showing that light propagation in non-linear media in the presence of a moving refractive index perturbation can lead to a gravity-dependent blueshift. We find that the predicted blueshift surpasses the gravitational redshift even if the medium is considered to be perfectly stiff. In realistic scenarios, by far the strongest frequency shift arises due to the deformation of the dielectric medium and the corresponding photoelastic change of refractive index. This has the potential to facilitate optical sensing of small gravity gradients.
[1] Alessio Belenchia, Felix Spengler, Dennis Rätzel, Daniel Braun, New J. Phys. 26 083010 (2024)

Abstract: Numerical evolutions show that, in spherical symmetry, as we move through the solution space of GR to the threshold of black hole formation, the resulting spacetimes tend to display a surprising degree of simplicity. A heuristic description of this behavior, called critical collapse, has been built around this empirical fact. Less is known when symmetry is dropped. In this presentation I will review the current status of the topic, focusing in particular on the struggle to understand the situation in axisymmetry.

We show that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’, or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.

Abstract: According to Rytov's law, the polarization vector of light follows a Fermi-Walker transport equation in optical fibers. Recent advancements in theory propose a modification to Rytov's law due to fiber bending. The aim of this talk is to further extend these predictions from flat to curved space-time. This involves perturbatively solving Maxwell's equations under the assumption that the wavelength is significantly shorter than the fiber's radius of curvature, as well as the characteristic length-scales of the ambient space-time. This results in a coupling of the polarization vector to the spatial Riemann curvature tensor and second derivatives of the lapse function.

Abstract: The study of existence and multiplicity of time-periodic solutions for semilinear Klein-Gordon equation has recently been proposed as a toy model to understand stability properties of Anti-de Sitter spacetime under certain perturbation, a question which is of great interest in general relativity. I will present a result on existence and multiplicity of Cantor families of small amplitude, analytic in time and periodic solutions for the completely resonant cubic nonlinear Klein-Gordon equation on S3 for an asymptotically full measure set of frequencies. The solutions are constructed by a Lyapunov- Schmidt decomposition and a Nash-Moser iterative scheme. We first find non-degenerate solutions of the resonant system, then, in view of small divisors problem, we solve the Range equation by a Nash-Moser iteration.

Abstract: Conformally invariant scalar equation allows one to impose the Robin boundary condition at infinity in asymptotically-AdS spacetimes. In our work, we show how the dynamics of conformal cubic scalar field on the Schwarzschild-anti-de Sitter background depend on the black hole size and the choice of the boundary condition. We also discuss the work in progress regarding the charged black hole case. This is joint work with Maciej Maliborski.

Abstract: In this talk I will present two recent results on the construction of initial data solving the constraint equations and which suits the decay requirements of either Minkowski stability or Kerr stability. The Minkowski result is the most technical since KIDS are handle by Kerr asymptotics, the control of which requires some work. The Kerr result benefits from the presence of the event horizon and the freedom in choosing the boundary condition for the conformal method. In particular, we are able to completely avoid the KIDS. This is joint work with Allen Juntao Fang and Jérémie Szeftel.

Abstract: Isolated gravitational systems such as stars, galaxies and black holes are modeled by asymptotically flat initial data sets. In 1981 Schoen-Yau and Witten showed that such initial data sets with vanishing energy must be contained in Minkowski space. We show that if such initial data sets have vanishing mass, they must be contained in pp-wave spacetimes. This is based upon joint work with Yiyue Zhang from UCI.

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Abstract: We present recent progress in understanding the dynamical behaviour of relativistic fluids in cosmological spacetimes. In particular, we show how the relation between expansion rate of the Universe and speed of sound of the fluid affect the stability of homogeneous fluid states.

Abstract: One is probably aware that classification of RCFTs has been studied at a steady and formal pace over the past few decades. But often when we are asked to define or characterize an RCFT who target spaces are X, there are different answers and characterisations. (X can be an abelian variety like a torus, or a an algebraic variety like K3 surfaces etc.) Phenomenologically, rationality can explain things like electroweak gaugino dark matter, gauge coupling unification and small gravitino mass, and attribute them to large chiral algebra on the worldsheet string theory, and not to a larger symmetry of the spacetime field theory. Mathematically, Rational CFTs provide a physical way to determine points of arithmetic in the moduli space of a variety. For the case of X = d dimensional tori, these various characterisations as I will explain are equivalent if and only if there are further conditions imposed and provide a sketch of proof. I will also discuss possible connections to random matrix theories and arithmetic of abelian varieties if time permits.

Abstract: In this talk I will show that there are vacuum static 3+1 black hole solutions, metrically complete but non-standard spatial topology, that cannot be put into stationary rotation. That is, there are no non-static stationary metrics close to them. To our knowledge, this is the first result of this kind in the literature. This is joint work with Javier Peraza.

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Abstract: In this talk, I will describe recent and upcoming work on the asymptotic behaviour of gravitational radiation (linearised gravity around Schwarzschild) in a neighbourhood of spacelike infinity including past and future null infinity. I will first set up a mathematical scattering framework in which one can understand the question of smoothness of null infinity on physical grounds. I will then use this framework to present a basic sketch of the proof of the irregularity of null infinity in various physically motivated settings, together with a complete description of the semiglobal asymptotics of gravitational radiation one obtains instead. In particular, I will discuss how a class of asymptotic conservation laws related to the Newman-Penrose charges can be used to infer the asymptotics for fixed angular modes, and describe how to use a persistence of polyhomogeneity result to sum up the individual angular modes. Based on joint work with Hamed Masaood and Istvan Kadar.

Abstract: Linear perturbations of black holes have been discussed widely in many contexts. Of interest are properties such as differential cross-sections or quasi-normal modes. A useful tool in this respect is the Newman-Penrose formalism and the resulting Teukolsky equations, giving seperated angular and radial differential equations. These were mostly evaluated by numerical means or in approximations. However, the introduction of a cosmological constant allows the problem to be solved in an exact analytical manner by transforming the differential equations into the Heun differential equation, the most general second-order differential equation with four regular singularities. We show for the Kerr-de Sitter spacetime that scattering of waves from a point source needs an additational discussion around the so-called Heuns function, which enables a then possible normalization of the angular solution, similarly to the case of spherical harmonics. We assume in the discussion and analysis a scalar source star of fixed frequency and solve the scattering problem by a partial wave sum. The observed wave optical image formation by means of Kirchhoff-Fresnel diffraction and the resulting shadow will be compared to e.g. the ray-optical black hole shadow.

Abstract: I will present a method of determining the mass density along the line of sight using variations of times of arrival of electromagnetic signals, as measured by two ensembles of free falling, precise clocks. The whole set-up may be considered a type of an extended gravitational compass, i.e., a device measuring directly the spacetime curvature using an ensemble of communicating clocks. I will also discuss the geometric interpretation of this measurement.

Abstract: Gravitational waves can generally influence the dynamics of test objects with which they interact. Changes in the relative dynamics of test objects can persist even after the gravitational wave has passed and spacetime is again flat. These are generally referred to as gravitational memory effects, since the properties of the passing gravitational wave remain encoded in the relative dynamics of test objects. In this talk, I will discuss gravitational memory effects in plane wave spacetimes for different classes of test objects: particles following geodesics, spinning particles with non-geodesic motion, and test scalar fields. For all these objects, memory effects are encoded into a set of four memory tensors that depend on the gravitational wave profile. Joint work with Abraham Harte, Thomas Mieling, and Florian Steininger.

Abstract: I review the 3+1-decomposition of GR or other field theories done in such a way that the time leaves need not form a foliation, i.e. where the lapse function can become zero or even change sign. I make remarks on local existence as well as on the relation with the 'hypersurface deformation algebra' put forward by Teitelboim, Kuchar and others.

Abstract: In this talk I will study the necessary and sufficient conditions that a spacetime admitting a bifurcate Killing horizon must satisfy to be static, i.e. such that the Killing of the horizon is hypersurface orthogonal. The result involves a bulk condition on the Ricci curvature, which is automatically satisfied for $\Lambda$-vacuum spacetimes, and a boundary condition on the data at the bifurcation surface. The problem is solved in arbitrary dimension, and requires a different treatment in the region where the Killing is timelike (the exterior of the horizon) or spacelike (inside the horizon). This is joint work with Piotr. T. Chrusciel.

Abstract: In a series of work, Aretakis, Czimek, and Rodnianski have studied the gluing of two sets of initial data to the Einstein equations along a null surface. By solving the linearized gluing problem around Minkowski and using the implicit function theorem, they have shown that two sets of C2 “sphere data” sufficiently close to Minkowski can be glued together along a null surface up to a ten dimensional obstruction space. In this talk, I will present a generalisation of this result to (i) higher dimensions, (ii) include the cosmological constant and (iii) the gluing of higher regularity Ck data.
Based on joint work with Piotr Chrusciel and Finnian Gray arXiv:2401.04442 [gr-qc]

Abstract: We study the dynamics of a self-interacting spherically symmetric scalar field propagating on the Schwarzschild-anti-de Sitter background. We consider two parameters in the model: the size of the black hole and the Robin boundary parameter. In addition, we study both the focusing and defocusing nonlinearities. We find a pitchfork bifurcation in the defocusing case and for the focusing nonlinearity, a region of the phase space where all solutions blow up in finite time. An extensive study of static solutions and their linear stability allows us to provide a precise asymptotic description of global-in-time solutions and solutions near the threshold of finite-time blowup. This work is a first step in extending arxiv.org/abs/2001.03980 to asymptotically anti-de Sitter black hole spacetimes. Based on arxiv.org/abs/2312.02760.

Abstract: I will describe a differential graded Lie algebra tailored to study perturbations of Minkowski spacetime, including asymptotics. This differential graded Lie algebra is defined on the conformal compactification of Minkowski spacetime. Its Maurer-Cartan equation is equivalent to the vacuum Einstein equations, and is symmetric hyperbolic including across the boundary of Minkowski spacetime. I will compare this to Friedrich's conformal vacuum field equations, a key difference is that we do not use a conformal factor as an unknown, and null infinity is a fixed locus independent of the unknown. I will then introduce an iteration scheme that gives an order-by-order construction of formal power series solutions about Minkowski. This is based on standard Maurer-Cartan perturbation theory and renormalization of the mass and angular momentum charges. The gauge character is naturally built into the setup. The algebraic framework allows for a rigorous contact with the physics literature on scattering amplitudes. We will see, in low order formal perturbation theory, that these gauge independent amplitudes describe the radiative null asymptotics of the formal solutions.

Abstract: Symplectic singularities, also known as hyper-Kahler singularities, encompass well-known geometric spaces such as the Kleinian surface singularities or the moduli space of instantons. Recently, a new class of symplectic singularities has emerged through the construction based on a physics model known as the 3d N=4 Coulomb branch. In this talk, I aim to provide an introduction and overview of symplectic singularities in general, with a particular focus on the 3d N=4 Coulomb branches. I will place special emphasis on the symplectic singularities that manifest as moduli spaces of vacua within supersymmetric field theories containing 8 supercharges in space-time dimensions ranging from 3 to 6. These instances showcase how geometric features offer elegant descriptions of strongly coupled phenomena.

Abstract: It is known that a source-free Yang-Mills theory with the normal conformal Cartan connection used as the gauge potential gives rise to equations of motion equivalent to the vanishing of the Bach tensor. We investigate the conformally invariant presymplectic potential current obtained from this theory and find that on the solutions to the Einstein field equations, it can be decomposed into a topological term derived from the Euler density and a part proportional to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of our potential to the asymptotic boundary of asymptotically de Sitter spacetimes turns out to coincide with the current obtained from the holographically renormalized gravitational action. This provides an alternative derivation of a symplectic structure on scri without resorting to holographic techniques. We also calculate our current at the null infinity of asymptotically flat spacetimes and in particular show that it vanishes for variations induced by the BMS symmetries. In addition, we calculate the Noether currents and charges corresponding to gauge transformations and diffeomorphisms.

Abstract: To a first approximation, objects in general relativity move along geodesics. Looked at more closely, a body's internal structure affects its motion, causing different objects to fall in different ways. This talk will explore what is possible and what is not in that context. For example, it is possible for a suitably-engineered spacecraft to change its orbit purely by changing its shape. Still, there are constraints. I will discuss how all such constraints arise from a very weak type of "local symmetry." Constraints arise from the presence of Killing vectors and from conformal Killing-Yano tensors, but from much more as well.

Abstract: One of the important extensions of Riemann geometry is Weyl geometry, which is essentially based on the ideas of conformal invariance and nonmetricity. A similar non-Riemannian geometry was proposed by Erwin Schrödinger in the late 1940s, in a geometry which is simpler, and (probably) more elegant than the Weyl geometry. Even it contains nonmetricity, the Schrödinger connection preserves the length of vectors under parallel transport, and thus seems to be more physical than the Weyl connection. Interestingly enough, Schrödinger's approach did not attract much interest in the field of gravitational physics. It is the goal of the present talk to reconsider the Schrödinger geometry as a potential candidate for a gravitational theory extending standard general relativity. We consider a gravitational action constructed from a length preserving non-metricity, in the absence of torsion, and investigate its variation in both Palatini and metric formalisms. While the Palatini variation leads to standard general relativity, the metric version of the theory adds some non-metricity dependent extra terms in the gravitational Einstein equations, which can be interpreted as representing a geometric type dark energy. After obtaining the generalized Friedmann equations, we analyze in detail the cosmological implications of the theory, by considering two distinct models, corresponding to a dark energy satisfying a linear equation of state, and to conserved matter energy, respectively. We compare the predictions of the Weyl-Schrödinger cosmology with a set of observational data for the Hubble function, and with the results of the λ standard paradigm. The Weyl-Schrödinger cosmological models give a good description of the observational data, and, for certain values of the model parameters, they can reproduce almost exactly the predictions of the λ model. Hence, the Weyl-Schrödinger theory represents a simple, and viable alternative to standard general relativity, in which dark energy is of purely geometric origin.

Abstract: De Sitter space-time is a geodesically complete, conformally flat, spatially compact solution to the Einstein-λ-vacuum equations with cosmological constant λ that admits smooth conformal boundaries ${\cal J}^{\pm}$ at future and past time-like infinity. Data sufficiently close to de Sitter data develop into solutions to the Einstein-λ-vacuum equations that admit smooth conformal boundaries as well. These solutions extend, as solutions to the conformal Einstein equations, beyond these boundaries where they define again solutions to the Einstein-λ-vacuum equations. Gravitational radiation, i.e. perturbations to the conformal Weyl tensor, travels unimpeded across ${\cal J}^{\pm}$ into the extended domain. In this talk we discuss our interest in this phenomenon and the question to what extent it generalizes to the future developments of solutions to the Einstein-λ equations coupled to various matter fields.

Abstract: I will present a recent proof which shows that the intrinsic geometry of compact cross-sections of any vacuum extremal horizon, possibly with a cosmological constant, must admit a Killing vector field. In particular, this implies that the extremal Kerr horizon is the most general such horizon in four-dimensional General Relativity and completes the classification of the associated near-horizon geometries.  I will also discuss a recent uniqueness proof which shows that any analytic Einstein spacetime, that contains a static extremal horizon with a maximally symmetric compact cross-section, is the extremal Schwarzschild de Sitter spacetime or its near-horizon geometry.

Abstract: Despite the absence of a lightcone structure, some solutions of Carroll gravity show black hole-like behaviour. I define Carroll black holes as solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface, notions I will introduce in this talk. The latter is a Carroll analogue of a Lorentzian extremal surface. Finally I will discuss some examples like the Carroll version of the Schwarzschild black hole.

Abstract: It is well-known that spherically symmetric steady states of the Vlasov-Poisson system can be obtained as minimizers of an energy-Casimir functional. This has played an important role for the celebrated stability results in that case. It is also well-known, cf. the recent review paper by Rein arXiv:2305.02098, that there are no analogue results for the Einstein-Vlasov system, mainly due to lack of compactness. In this talk I will close this gap by showing compactness of minimizing sequences to a particle-number-Casimir functional, which then implies the existence of a minimizer. Under a regularity assumption it follows that the minimizer is a steady state of the spherically symmetric Einstein-Vlasov system. As a consequence of the proof, a condition arises which we believe is sufficient for non-linear stability. All claimed conditions of this type have so far been disproved in numerical studies. This is a joint work with Markus Kunze.

Abstract: In my talk, a null geometric approach to the quasilocal Brown-York formalism will be used to calculate, within a bounded gravitating physical system, the flux of energy through a dynamical horizon of a non-stationary spacetime. This is done by varying the total Hamiltonian of the system (bulk part plus boundary part) so as to derive an integral law describing the rate of change of mass and/or radiant energy escaping through the dynamical horizon. The results obtained in this way, as is shown, lead to previously unrecognized correction terms, including a bulk-to-boundary inflow term that leads to corrective extensions of Einstein's quadrupole formula in the large sphere limit and to quasilocal corrections to Bondi's mass-loss formula, the latter occurring in the null geometric context. Specific applications in the areas of gravitational wave physics and the theory of tidal heating and deformation effects are discussed.

Abstract: We try to develop a method for constructing ''Love symmetry'' generators in rotating black hole spacetimes of general dimensions. After revisiting the 4D Kerr and 5D Myers–Perry cases, we apply it generalized Lense-Thirring spacetimes which describe a wide variety of slowly rotating black hole metrics in any number of dimensions.

Abstract: We consider 4-dimensional, Ricci-flat and asymptotically flat (AF) manifolds with metrics of either Lorentzian or Euclidean signature, and with a 1-parameter group of isometries whose Killing tangent vectors have bounded length at infinity. If non-flat we call such Lorentzian solutions stationary AF black holes (SBHs), and the Euclidean ones S1-AF instantons (SGIs). The latter play a role in the path integral approach to Quantum Gravity which we review briefly. We then recall known examples of SBHs and SGIs. We continue with explaining the "nuts and bolts" classification of SGIs which is the Euclidean counterpart to stationary and static black hole horizons. We next review the Kerr uniqueness results, which read that analytic, connected SBH must be Kerr, and that SGIs with 2 nuts must be Euclidean Kerr. We also discuss the family of SGIs found by Chen and Teo which have 3 nuts and no real Lorentzian counterparts. As a step towards a conjectured uniqueness result for this family, we show that any SGI with "Chen-Teo topology" must be "half algebraically special". We finally sketch uniqueness results for stationary black holes and S1-instantons with are locally asymptotically flat rather than AF.

Abstract: We construct the first four-dimensional multi-black hole solution of general relativity with a positive cosmological constant. The solution consists of two static black holes whose gravitational attraction is balanced by the cosmic expansion. These static binaries provide the first four-dimensional example of non-uniqueness in general relativity without matter.

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Abstract: Maximal Surfaces are spacelike hypersurfaces of a Lorentzian manifold which are critical points of the area functional. They are very important tools in General Relativity and can be studied by applying non-linear PDEs techniques since the Euler-Lagrange equation of the variational problem of maximization of the area is a quasi-linear elliptic PDE that geometrically describes the vanishing of the mean curvature. Given the behavior of some simple solutions in Minkowski Spacetime, it seems natural to investigate when sequences of Maximal Surfaces on exterior domains converge to Null Hypersurfaces. We will present some developments in this direction, starting with a discussion on the existence of solutions over exterior domains in static spacetimes.

Abstract: The threshold of black hole formation in parametrized families of collapse models exhibits many of the features of a phase transition. Universality and scaling behaviour are generically observed and a picture of critical phenomena emerges, completely analogous to that seen in statistical mechanical systems.
Most of the studies of critical collapse have been performed in the context of spherical symmetry where a relatively clear picture of the phenomenology has arisen. In particular, the critical solutions that are found tend to be (locally) unique, with some additional symmetry, and with a single unstable mode in perturbation theory.
Going beyond spherical symmetry in this field has proven to be quite challenging, and an overall understanding of the nature of non-spherical critical collapse remains elusive. Nonetheless, some progress has been made recently on models involving the collapse of pure gravitational waves as well as electromagnetic waves. My talk will focus on these developments.

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Abstract: See title.

Abstract: I will give an introduction to Fröhlich's Events, Trees, Histories (ETH) approach to quantum theory. I will then introduce the causal compatibility conjecture. Applying it to spacetimes with closed causal curves we find that time travel is boring. Finally I will introduce the open problem in mathematical relativity underlying the causal compatibility conjecture.

Abstract: Ultra light dark matter is an interesting model where the mass of the particle is so light that wavelike phenomena manifest on astrophysical scales. Here we operate on the interface between cosmology and quantum mechanics. Simulations have emerged as one of the most powerful methods for studying this model. Typically, classical field theory is used to simplify the numerics of the problem on a wide variety of time and length scales. However, the applicability of this approximation on some of these scales has become a subject of some debate in the literature. The numerical complexity of quantum mechanical simulations has resulted in much of the previous work on this topic relying on analytic approximations or small toy systems. In this talk we will discuss the truncated Wigner approximation, a highly parallelizable method that can be used to study quantum corrections for test problems many orders of magnitude larger than has been previously studied in the context of ultra light dark matter. We will show how this method can be used to reliably estimate quantum corrections to the classical field theory, as well as estimate the decoherence time for a dark matter system coupled to Baryonic matter.

Abstract: In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to positive Ricci curvature for m =  1, and positive scalar curvature for m = n-1) on closed orientable manifolds with topology $N^n = M^{n-m} x \mathbb{T}^m$ for $n \leq 7$. Our proof uses a slicing constructed by minimization of weighted areas, the associated stability inequality, and estimates on the gradients of the weights and the second fundamental form of the slices. This is joint work with Simon Brendle and Sven Hirsch.

Abstract: Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which is possible in theories admitting regular black holes with de Sitter-like interiors.
In this talk, I will show how this scenario can be considerably strengthened by placing it in a global anti-de Sitter background, where the formation of "de Sitter bubbles" will be enhanced by mechanisms analogous to the Bizon&Rostworowski instability in general relativity.

Abstract: We study the scalar, conformally invariant wave equation on a Schwarzschild background, which can be considered as a toy model for the conformal field equations for spacetimes with black holes. Even though the wave equation is a much simpler equation, it already mirrors important mathematical properties and difficulties of the general problem. Our main interest is in a suitable treatment of spatial infinity, which is represented as a cylinder. Firstly, we consider the Cauchy problem for the wave equation. We study a family of equations intrinsic to the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many expansion orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that a fully pseudospectral time evolution scheme can be applied to solve the Cauchy problem numerically. In this approach, spectral expansion with respect to space and time are used, and the solution is obtained at all grid points simultaneously. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to future null infinity from the critical set, where the cylinder approaches null infinity. Secondly, we also investigate the characteristic initial value problem for the wave equation. Here, the intrinsic cylinder equations require initial data that are not immediately available from the characteristic initial data. They can only be obtained if we also study the behaviour of the solutions near past null infinity. This allows us to construct families of characteristic initial data for which the time-evolution will have any desired finite degree of regularity.

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Abstract: To test the theory of gravity one needs to test, on one hand, how space and time are distorted by matter and, on the other hand, how matter moves in a distorted space-time. Current observations provide tight constraints on the motion of matter, through the so-called redshift-space distortions, but they only provide a measurement of the sum of the spatial and temporal distortions, via gravitational lensing. In this talk I will present a novel method to measure the time distortion on its own, and I will show that it will be detectable by future surveys like the SKA. I will then discuss new tests of gravity that can be build from this measurement.

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Abstract: Previous theoretical models of fiber optics in gravitational fields were limited to specific fiber geometries. Using a recently-developed multiple-scales method, however, one can solve Maxwell’s equations for arbitrarily bent optical fibers in arbitrary stationary space-times, provided that the characteristic length scales of the fiber geometry and the gravitational field far exceed the optical wavelength. The focus of this talk is on two key effects relevant to the future GRAVITES experiment: the gravitational redshift and the Sagnac effect, which are derived from the lapse and the tangential shift, respectively. Further corrections arising, e.g., from spatial curvature, shall be discussed briefly if time permits.

Abstract: The quest for physics beyond the standard models of cosmology and particle physics is the primary motivation for upcoming observatories in space and on earth. The cosmic large-scale structure provides a unique testing ground for connecting fundamental physics to astronomical observations. A detection of the signature of massive neutrinos, deviations from Einstein’s theory of gravity, physical insights into the earliest inflationary phase of the Universe and the microphysical nature of dark matter and dark energy are all within the potential reach of these experiments in the next decade. In order to accurately link observations to fundamental physics, analytical, numerical, and data-driven techniques will be used. I will give a general introduction and discuss recent progress at the interface between numerical simulations and analytical calculations that enable faster and more robust predictions of the matter distribution in our Universe.

Abstract: We will start with a brief discussion about the role of self-similarity for the Einstein vacuum equations and then will introduce our new class of twisted self-similar solutions. The key defining feature of these new self-similar solutions is that while the homothetic vector field is tangent to the past light cone of the origin of dilation symmetry, it does not coincide with the null generators of this hypersurface and instead ``twists'' around the light cone. We will explain how to compute formal power series for these twisted self-similar solutions and discuss some applications.

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Abstract: The aim of this talk is to present aspects of the theory of (marginally, outer) trapped surfaces and sets. A closed spacelike surface in a spacetime is called trapped if both congruences of normal (future directed) null geodesics are converging. If the spacetime contains such a trapped surface, satisfies the null energy condition and admits a non-compact Cauchy surface, the spacetime is singular by Roger Penrose’s singularity theorem. Marginally outer trapped surfaces (MOTS) serve as a generalisation of trapped surfaces, in the sense that one of the null congruences has zero convergence. They are an integral part in the mathematical study of black holes.
Here we focus on the issue of (non-)visibility of MOTS from conformal future null infinity and explain corresponding known results especially in asymptotically de Sitter spacetimes. Next we restrict attention to de Sitter space itself and discuss MOTS of spherical and toroidal topology and their (non-)visibility. Finally we explain why the singularity theorems do not apply in this case.

Abstract: It has become one of the major endeavors in physics to understand the interplay between two of our most successful theories, quantum mechanics and general relativity. These efforts have to be guided by experiments and observations at the interface of the two theories. In this talk, I will present two specific examples of experimental proposals: a) A potential route to obtain evidence for quantized gravity by employing gravitationally coupled quantum optomechanical sensors [1]. b) An investigation of the effect of gravitational time dilation on photonic states stored in quantum memories [2]. I will also discuss the prospects to perform the corresponding experiments with near-future technology.
[1] Plato, A. D. K., Rätzel, D., & Wan, C. (2022). Enhanced Gravitational Entanglement in Modulated Optomechanics. arXiv:2209.12656.
[2] Barzel, R., Gündoğan, M., Krutzik, M., Rätzel, D., & Lämmerzahl, C. (2022). Gravitationally induced entanglement dynamics of photon pairs and quantum memories. arXiv:2209.02099

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Abstract: In this lecture, we aim to present some rigidity results for compact initial data sets, in both the boundary and no boundary cases. For example, under natural energy, boundary, and topological conditions, we obtain a global version of a well-known result of H. Bray, S. Brendle, and A. Neves. We also prove some extensions of results obtained, in a previous work, by M. Eichmair, G.J. Galloway, and the author. Finally, as time permits, we are going to present a number of examples in order to illustrate some of the results presented in this lecture. This is part of a joint work with G.J. Galloway.

Abstract: Wigner function are well known in quantum mechanics where they can be used as an alternative phase space description for the usual Schrodinger wave function. I will discuss how Wigner functions can be generalized for scalar waves on curved spacetime and how wave dynamics can be determined by solving an asymptotic series of transport equations along the geodesic flow. I will try to argue that the Wigner function formalism represents a useful approach for semiclassical analysis and wave effects beyond geometric optics, and, particularly in general relativity, it is related to massless Vlasov matter and Burnett’s conjecture. Mostly based on doi.org/10.1063/1.2200143 and doi.org/10.1007/s00023-020-00890-9.

Abstract: We present the first examples of formally asymptotically flat black hole solutions with horizons of general lens space topology L(p,q). These 5-dimensional static/stationary spacetimes are regular on and outside the event horizon for any choice of relatively prime integers 1 ≤ q < p in particular conical singularities are absent. They are supported by Kaluza-Klein matter fields arising from higher dimensional vacuum solutions through reduction on tori. The technique is sufficiently robust that it leads to the explicit construction of regular solutions, in any dimension, realising the full range of possible topologies for the horizon as well as the domain of outer communication, that are allowable with multi-axisymmetry. Lastly, as a by-product, we obtain new examples of regular gravitational instantons in higher dimensions. This is joint work with Jordan Rainone.

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Abstract: Within geometrical optics, Rytov’s law states that the polarization vector is Fermi–Walker transported along light rays. A transport law of this kind was experimentally observed in optical fibers – a regime in which ray optics does not suffice, but wave optics is required. In this talk, I will present a perturbative solution to the full Maxwell equations in arbitrarily bent fibers, under the sole assumption that the fiber’s radius of curvature is much larger than its diameter. At leading order, this provides a rigorous derivation of Rytov's law. At next order, one obtains non-trivial dynamics of the electromagnetic phase and polarization. We discuss potential experiments signatures of of these corrections and compare with similar results on this subject. This is joint work with Marius Oancea. arXiv:2302.10540 [physics.optics]

Abstract: There are a number of reasons due to which it is advantageous to have a phase space based, or microlocal, approach available for analyzing wave propagation. In this talk I will explain a microlocal framework for wave propagation on asymptotically flat spacetimes of arbitrary dimension which in particular includes operator corresponding to Lorentzian metrics arising from solutions of Einstein’s equations in the 4 spacetime dimensional setting. On the compactification of Minkowski space that underlies this, which is a manifold with corners (with the usual null infinity, scri, being a boundary hypersurface), the operators lie in a combination of Melrose’s totally characteristic (also called b), and Mazzeo’s edge pseudodifferential operator algebras. I will give an introduction via a simpler setting (which includes Minkowski space and a different class of perturbations), and then explain the reasons for, and complications with, moving to the present setting. This is joint work with Peter Hintz.

Abstract: I will discuss the difficulties associated with the definition of the energy in the radiating regime for linear theories on a de Sitter or anti de Sitter background.

Abstract: I will review some classical arguments concerning the remoteness of direct graviton detection. Treating gravity classically, the question arises how to consistently and reliably estimate the influence of classical gravitational fields on the dynamics of quantum systems. A review of the latter is given in https://arxiv.org/pdf/2207.05029.pdf

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Abstract: In this talk, I will present a rigorous construction of examples of black hole formation which are exactly isometric to extremal Reissner-​-Nordström after finite time. In particular, our result can be viewed as a definitive disproof of the ``third law of black hole thermodynamics.’’ This is based on joint work with Ryan Unger (Princeton).

Abstract: I will discuss the question of gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions d≥4, with emphasis on characteristic data.
Based on joint work with Wan Cong, arXiv:2302.06928 [gr-qc]

Abstract: The strong cosmic censorship hypothesis asserts that the inner horizons of Kerr-Newman(-deSitter) black holes are unstable against classical perturbations, thus effectively eliminating any problems with causality and determinism associated with the regions beyond the inner horizon. I discuss the status of this conjecture and emphasise the importance of quantum effects to avoid violations of strong cosmic censorship in the presence of a (positive) cosmological constant.

Abstract: Matter structures are among the key observations on large scales. Hence, their formation, or lack thereof, in certain mathematical models provides insight into whether these models are physically valid. In this talk we explore structure formation utilizing the tools of modern PDE analysis. Due to work by D. Christodoulou, it is known that the relativistic Euler equations are unstable for a rather comprehensive class of equations of state on Minkowski space. However, solutions exist globally for exponentially expanding FLRW-type models or even power law expansion, as was explored in the previous decade by J. Speck among many others. In our paper on dust as well as our followup on massive fluids, we prove that the homogeneous fluid solutions coupled to the Milne-universe are fully nonlineary stable solutions to the coupled Euler-Einstein-system with a linear equation of state. In particular, this shows that even linear expansion is sufficient for regularizing dust and massive fluids. This is joint work with David Fajman, Todd Oliynyk and Zoe Wyatt.

Abstract: Stationary Rotating black holes have two kinds of symmetries. The Explicit kind which are generated by their timelike and rotation Killing vectors, and the hidden ones which come from Killing tensors.These symmetries are very useful for simplifying physical equations because they enable one to apply a separation of variables ansatz decoupling the PDEs into a set of ODEs. In this talk I will review the general theory of separability in this context and how it applies to the Kerr--NUT--AdS class of spacetimes in any dimensions. There, the hidden symmetries all descend from one object called the principal tensor. As applications I'll discuss two pieces of work from my PhD: 1) the separability of the conformal wave equation in these Kerr--NUT--AdS spacetimes and 2) The hidden symmetries of a generic class of slowly rotating black holes.

Abstract: Nonlinear Schrödinger equations has been thoroughly investigated by physicists and mathematicians over the years. However, most of these results apply only to the lower dimensions, probably because of the lack of an apparent physical motivation to deal with dimensions higher than three and the breakdown of typically used mathematical tools in supercritical dimensions. In this seminar I want to motivate investigations of the titular equations by connecting them with some open problems in general relativity and mathematical physics. Then I will briefly present the key results from my PhD thesis regarding existence, uniqueness, and other properties of the stationary solutions. I will also touch the subject of the time-dependent solutions. In the end I want to give an outline of the potentially interesting directions for the future studies.

Abstract: We describe a localized gluing result for the constraint equations in which a small mass rescaling of an asymptotically flat data set is glued into the neighborhood of a point inside of another data set. As the smallness parameter tends to zero, rescalings of normal coordinates around the point become asymptotically flat coordinates on the asymptotically flat data set. As an application, we construct initial data for the Einstein vacuum equations which conjecturally evolve into extreme mass ratio inspirals.

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Abstract: I will discuss a spherically symmetric gravitating model that exhibits turbulent dynamics, conjectured to be the core mechanism of instability of the anti-de Sitter solution. Using the resonant approximation, I will provide evidence that generic arbitrarily small initial perturbations of amplitude epsilon lead to a black hole formation on the timescale 1/epsilon^2. Furthermore, I will argue that the perturbative approximation remains valid up to apparent horizon formation.

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Abstract: In this talk I will discuss an extension of Dain's construction of geometric invariants characterising stationarity to the case of initial data sets for the Einstein equations corresponding to black hole spacetimes. We prove the existence and uniqueness of solutions to a boundary value problem showing that one can always find approximate Killing vectors in black hole spacetimes and these coincide with actual Killing vectors when they are present. Moreover, I will discuss the relation between the boundary data for the approximate Killing vector equation and the notion of stability for MOTS.

Abstract: We present a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to previous constructions, the new perspective actively utilizes the nonlinearity of the constraint equations. As a result, we are able to remove the 10-dimensional spaces of obstructions to gluing present in the literature. As application, we show that any asymptotically flat spacelike initial data set can be glued to Schwarzschild initial data of sufficiently large mass. This is joint work with I. Rodnianski.

Abstract: In recent years, Fuzzy dark matter (FDM) became the subject of many studies because it may alleviate the small scale problems of cold dark matter (CDM). In this talk, I will present the background and the results of simulations conducted on the VSC, in which I focused on the dynamics of a point mass orbiting in FDM halos in order to study dynamical friction and other relaxation effects. Modelling these effects is important to understand for example the orbital decay of a supermassive black hole towards the center of a galactic halo. Another example is the heating of stars in dwarf galaxies, where currently only theoretical predictions are used to derive constraints on the FDM particle mass. Similar numerical simulations were previously only performed for point masses orbiting in FDM solitons. My work extends this to galactic halos. The simulation results showed that even very massive test objects do not sink completely towards the halo core but instead the objects stop inspiraling at some distance from the center as predicted by theor

Abstract: Just like light, gravitational waves (GWs) are deflected and magnified by the large-scale structure of the Universe, a phenomenon known as gravitational lensing. Their low frequency, phase coherence and capacity to propagate with no absorption makes GWs an ideal signal in which to observe wave-propagation phenomena. I will describe how GWs deflected by cosmic structures produce diffractive, wave-optics phenomena, whose measurement will allow us to infer the properties of galactic and dark matter halos. For GWs in strong gravitational fields, such as the vicinity of a massive black hole, their propagation depends on the frecuency (dispersion) and polarization (birefringence) through the gravitational spin-hall effect. I will describe how observations of sources near central black holes of galaxies may enable the observation of dispersive GWs. While birefringence might be too suppressed to observe in Einstein’s general relativity, alternative theories predict that the two GW polarizations travel at different speeds near massive objects. Searches for this effect provide one of the most stringent tests of gravity so far.

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Abstract: The ringdown and shadow of the astrophysically significant Kerr Black Hole (BH) are both intimately connected to a special set of bound null orbits known as Light Rings (LRs). Similarly, ultracompact objects with LRs but without an horizon could mimic BHs in some of their strong gravity phenomenology. However, are such ultracompact objects dynamically viable? Stationary and axisymmetric ultracompact objects that can form from smooth, quasi-Minkowski initial data must have at least one stable LR, which has been argued to trigger a spacetime instability. Until recently its development and fate had been unknown. We confirm that the LRs indeed triggered an instability in fully non-linear numerical evolutions of ultracompact bosonic stars free of any other known instabilities. The results shows that the LR instability can be effective in destroying horizonless ultracompact objects that could be plausible BH imitators.

Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory.
This talk is based on work with Stefan Hollands and Aron Kovacs.

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Abstract: In this talk I will discuss the “harvesting” of entanglement by two Unruh-DeWitt detectors from the massless scalar field vacuum in 3+1D Minkowski spacetime. In particular, I shall share some numerical results on how the amount of entanglement depends on the relative velocity between the detectors. We shall see that the entanglement gained by the detectors can be increased if one detector is moving with respect to the other.

Abstract: : In this talk, I will present the quantisation of the linear scalar field when the background spacetime metric is not smooth. The analysis of quantum fields in spacetimes, where the metric is not smooth, has two primary motivations. First, there are several models of physical phenomena that require spacetime metrics with finite regularity. Second, the analysis of the well-posedness of Einstein’s equations, viewed as a system of hyperbolic PDE’s requires spaces with finite regularity. I will focus mainly on the microlocal aspects of the causal propagator and the two-point function of ground states, and the techniques used to overcome the lack of smoothness. The talk is based on arXiv:1910.13789 and arXiv:2207.01429.

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Abstract: In this work we revisit the famous Fermi two-atom problem, which concerns how relativistic causality impacts atomic transition probabilities, using the tools from relativistic quantum information and algebraic quantum field theory. The problem has sparked different analyses from many directions and angles since the proposed solution by Buchholz and Yngvason (1994). Some of these analyses employ various approximations, heuristics, perturbative methods, which tends to render some of the otherwise useful insights somewhat obscured. It is also noted that they are all studied in flat spacetime. We show that current tools in relativistic quantum information, combined with algebraic approach to quantum field theory, are now powerful enough to provide fuller and cleaner analysis of the Fermi two-atom problem for arbitrary curved spacetimes in a completely non-perturbative manner. Our result gives the original solution of Buchholz and Yngvason a very operational reinterpretation in terms of qubits interacting with a quantum field, and allows for various natural generalizations and inclusion of detector-based local measurement for the quantum field (PRD 105, 065003).

Abstract: To understand to which extent cosmological models make sense as an approximation of our universe, it is of particular interest to study their stability within the Einstein equations. In this talk, I will present a recent result based on joint work with David Fajman, in which we prove that FLRW spacetimes with negative spatial sectional curvature and (non-trivial) spatially homogeneous scalar field are nonlinearly stable within the Einstein scalar-field system. This also verifies the Strong Cosmic Censorship conjecture (in a C²-sense) near these FLRW spacetimes in both the collapsing and the expanding direction, which we analyse separately:
Toward the Big Bang, one observes stable curvature blow-up that drives geodesic incompleteness. Crucially, this is shown with a covariant approach using Bel-Robinson variables that is largely independent of spatial geometry and may prove to be very robust when translated to other settings. Toward the future, near-FLRW solutions are future complete and asymptotically approach the vacuum Milne solution. This boils down to proving future stability of the Milne solution itself, which we then establish independently.

Abstract: It is well known that gravitational waves interact in a non-linear way. This makes it difficult to describe them rigorously. The cleanest description is based on a certain conformal invariance of the Einstein equations — a fact which was established by R. Penrose and was used by H. Friedrich to prove several important global results for general relativistic space-times. The so-called conformal field equations implement this conformal invariance on the level of partial differential equations. They provide various well-posed initial (boundary) value problems for use in different situations. The talk will give a computational perspective on the non-linear interaction of gravitational waves with an initially static (and spherically symmetric) black hole. We will show how to kick it and possibly how to spin it up. Time permitting, we will also discuss the emergence of quasi-normal modes and the Newman-Penrose constants.

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Abstract: The quest for dark matter is one of the most pressing questions of modern physics. We know that it exists, but its (particle) nature remains in the dark. Direct dark matter detection experiments aim to detect interactions of dark matter particles in earth-bound detectors. Despite tremendous improvement in sensitivity over the last decades, all experiments report null results except for the DAMA experiment. DAMA has observed since the 1990s an annually modulating event rate in their NaI detectors compatible with dark matter particles in the milky way. To resolve the contradicting results in direct detection, experiments with the same target material -- NaI -- are needed to be immune against material and model dependencies. COSINUS is one of these experiments, albeit the only one operating NaI as a cryogenic detector. In this talk, I will introduce the direct detection of dark matter with a particular focus on the DAMA claim and its cross-check with COSINUS.

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Abstract: General Relativity (GR) is immensely successful. With the late discovery of gravitational waves from black hole and neutron star mergers, it has passed all the tests with flying colors. But so far, observations have mainly tested the vacuum equations of GR. The most important non-vacuum case, cosmology, is in agreement with GR only after the introduction of two otherwise unknown components, 'Dark Matter' and 'Dark Energy' which amount to about 96% of the total energy budget of the present Universe. This lead people in the field to question the validity of GR for cosmology. Might it be that GR is flawed on large, cosmological scales? Or in the presence of matter in general?
But how can we test Einstein's equation in the presence of matter? Can't we simply move any modification of the Einstein tensor to the right hand side and call it a 'dark matter/energy' component?
In my talk I shall discuss possible ways (partially) out of this dilemma. How to test both, the left and the right hand side of Einstein's equations with cosmological observations

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Abstract: Asymptotically flat half-spaces (M,g) are asymptotically flat manifolds with a non-compact boundary. They naturally arise as suitable subsets of initial data for the Einstein Field equations. In this talk, I will present a proof of the Riemannian Penrose inequality for asymptotically flat half-spaces with horizon boundary (joint with M. Eichmair) that works in all dimensions up to seven. This inequality gives a sharp bound for the area of the horizon boundary in terms of the half-space mass of (M,g). To prove the inequality, we double (M, g) along its non-compact boundary and smooth the doubled manifold appropriately. To prove rigidity, we use variational methods to show that, if equality holds, the non-compact boundary of (M,g) must be totally geodesic. I will also explain how our techniques can be used to prove rigidity for the Riemannian Penrose inequality for asymptotically flat manifolds.

Abstract: The state of a quantum particle undergoing rapid measurements will be “frozen” in an eigenstate of the measurement. If a source is frozen via this way in a massive superposed state, a probe particle will experience a gravitational potential equal to that sourced by a mass density proportional to the square of the wavefunction of the quantum source. I will provide some back-of-the-envelop calculations to discuss the feasibility of measuring such a potential generated by O(10^-11) kg masses through classical scattering of probe particles.
On a separate topic, I will also discuss the “harvesting” of entanglement by two Unruh-DeWitt detectors from the scalar field vacuum in 3+1D Minkowski spacetime. In particular, I shall share some numerical results on how the amount of entanglement depends on the relative velocity between the detectors.

Abstract: Einstein-scalar-Gauss-Bonnet theories lead to second order field equations, that feature a wide variety of interesting compact solutions. Depending on the coupling function of the scalar field to the Gauss-Bonnet term, different types of solutions are obtained. In this talk I will focus on coupling functions, that allow the black hole solutions of General Relativity to remain solutions of the field equations, but that yield in addition scalarized solutions. Besides a variety of scalarized black hole solutions I will discuss also other types of compact solutions. These may feature light rings and echoes and quality as UCOs, ultra-compact objects.

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Abstract: Axion Dark Matter is one of the most promising dark matter candidates and in its ultralight limit (ULDM) exhibits unique interference phenomena on large cosmological scales. This model has initially proven very promising because of its potential to solve several of the small-scale problems of structure formation in cold dark matter. Recently, constraints on the mass of the corresponding particle have improved significantly. However, almost all constraints are based on the assumption that ULDM consists of a single complex scalar filed, which obeys the Schrödinger-Poisson equations.
In this talk I will discuss the possibility that ULDM is composed of several independent scalar fields, coupled only by gravity. I will demonstrate that the phenomenology of the resulting density field changes compared to the single field case and discuss implications on the constraints.

Abstract: I will present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These latter solutions are referred to as gravitational solitons. Further partially compactified solutions are also obtained by taking appropriate quotients, and the topologies are computed explicitly in terms of connected sums of products of spheres. In addition, it is shown that there is a correspondence, via Wick rotation, between the spacelike slices of the solitons and black hole solutions in one dimension less. As a corollary, the solitons give rise to complete Ricci flat Riemannian manifolds of infinite topological type and generic holonomy, in dimensions 4 and higher.
This is joint work with Marcus Khuri, Martin Reiris, and Sumio Yamada.

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Abstract: A long-standing problem in QFT and quantum gravity is the construction of an “IR”-finite S-matrix. In the gravitational case, the existence of these “infrared divergences” is intimately tied to the “memory effect” (i.e. the permanent displacement of test masses due to the passage of a gravitational wave) and the existence of an infinite number of conserved charges at spatial infinity. In this talk, I shall explain the origin of these connections and illustrate that the construction of an IR-finite S-matrix requires the inclusion of states with memory (which do not lie in the standard Fock space). In massive QED an elegant solution to this problem was provided by Faddeev and Kulish who constructed an incoming/outgoing Hilbert space of charged particles “dressed” with memory. However, we show that this construction fails in the case of massless QED, Yang-Mills theories, linearized quantum gravity with massless/massive sources, and in full quantum gravity. In the case of quantum gravity, we prove that the only "Faddeev-Kulish" state is the vacuum state. We also show that “non-Faddeev-Kulish” representations are also unsatisfactory. Therefore, in full quantum gravity, it seems that there does not appear to be any (separable) Hilbert space of incoming/outgoing states that can accommodate all scattering states. Therefore we argue that, if one wants to treat scattering theory at a fundamental level, one must take an "algebraic approach" which does not require an a priori choice of Hilbert space. We outline the framework of such an IR finite scattering theory.

Abstract: The notion of locality seems a priori in conflict with the gauge symmetries of gravitational theories -- i.e. a group of diffeomorphisms --, which move spacetime points around. A means of addressing this issue is to invoke dynamical reference frames, which provide field-dependent coordinatizations of spacetime. In this talk, I will describe a completely general framework for constructing such dynamical frames and their associated relational observables in generally covariant theories. These observables describe the remaining degrees of freedom in a gauge-invariant manner relative to the frame and give rise to a relational notion of locality, based on the relationships between fields. Our framework unifies previous approaches and naturally comes with the notion of relational atlases and dynamical frame transformations that permit us to change between arbitrary relational frame perspectives. This can be viewed as establishing a genuinely relational -- and thus arguably more physical -- update of the usual notion of general covariance. I will then comment on how dynamical frames can be used to formulate a relational form of microcausality and to define subsystems (i.e. subregions) in a gauge-invariant manner. In particular, the physical symmetries and corresponding charges associated with the subregion can be understood in terms of reorientations of the frame.

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Abstract: We derive the Penrose data for half-flat pp-waves and extend his original construction for the Weyl spinor of plane waves in terms of these data.

Abstract: Ultracold atoms and their non-equilibrium evolution present an ideal platform to study fundamental processes of quantum field theory and the relaxation dynamics of quantum many-body systems. Here, I will present recent results and future prospects for analogue quantum simulators based on effective field theory descriptions. In particular, I will discuss the measurement of the analogue circular Unruh effect via local interferometric two-frequency detectors [1,2]. The continuous non-destructive measurements of cold atom systems paves the way to study this fundamental and yet still untested prediction of quantum field theory, that a linearly accelerated observer in the vacuum observes a thermal state at the Unruh-temperature.

[1] C. Gooding, S. Biermann, S. Erne, J. Louko, W. G. Unruh, J. Schmiedmayer, S. Weinfurtner, Phys. Rev. Let. 125 213603 (2020)
[2] S. Biermann, S. Erne, C. Gooding, J. Louko, J. Schmiedmayer, W. G. Unruh, S. Weinfurtner, Phys. Rev. D 102 085006 (2020)

Abstract: General Relativity admits a well-posed characteristic initial value problem, where data is given on two transverse, null hypersurfaces. In this seminar, a new approach in which the initial data is defined abstractly and in a fully diffeomorphism and gauge-covariant way is presented. In order to achieve this we employ the so-called hypersurface data formalism, a framework in which one can study general hypersurfaces of any causal character from an abstract point of view (i.e. independent of any spacetime notion). Our abstract geometrization puts the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity, in the sense that the initial data has been completely detached from the spacetime one wishes to construct.

Abstract: Spin Hall effects represent a diverse class of physical phenomena related to the propagation of wave packets carrying intrinsic angular momentum. These effects have been experimentally observed in optics and condensed matter physics, but they are also expected to occur for wave packets propagating in gravitational fields. In this talk, I will introduce the equations of motion describing the gravitational spin Hall effect, and I will discuss their properties, physical interpretation, as well as the relation to the Mathisson-Papapetrou equations. Based on this, I will present recent results regarding the strong lensing of gravitational waves. Given the typical wavelengths of observed gravitational waves, the gravitational spin Hall effect is expected to have a significant effect that could lead to experimental observation.

Abstract: Currently there is a discrepancy between the Standard Model prediction for the anomalous magnetic moment of the muon and the experimental value above 4 standard deviations according to the Muon g-2 Theory Initiative White Paper. With further experimental improvements expected in the near future, it is imperative to further sharpen the theoretical prediction which is limited by uncertainties of QCD contributions. I describe the recent progress made in using gauge/gravity duality ("holographic QCD") to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models but are implemented naturally in simple ("bottom-up") holographic QCD models.

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Abstract: We study the Dirac equation for neutral particles with a magnetic moment in the field of an ultrashort electromagnetic pulse. The pulse is modeled as a delta-distribution, concentrated on a null (i.e. lightlike) hyperplane. We show that the solutions can be obtained by "gluing" free solutions along the pulse and derive corresponding matching conditions. For the special case of a homogeneous electromagnetic pulse, i.e. constant field strength, we explicitly calculate the change in the spin orientation. This is joint work with Peter C. Aichelburg and Herbert Balasin.

Abstract: I will discuss accretion of collisionless Vlasov gas onto a Schwarzschild black hole. An equivalent of the Bondi flow (steady spherically symmetric accretion) has been developed by Paola Rioseco and Olivier Sarbach in 2017. In this case, the gas is assumed to be at rest at infinity, where it is described by the Maxwell-Juttner distribution. Last year, together with Andrzej Odrzywołek, we computed an equivalent of the so-called Bondi-Hoyle model (accretion onto a moving black hole). I will discuss some details of this model and compare them to the results obtained in the ballistic approximation. If time permits, I will comment on possible generalizations to the Kerr geometry

Abstract: General Relativity and the Cosmological Principle are the fundamental pillars of Cosmology. After introducing them and their underlying properties I will discuss the successes and challenges of the Standard Model of Big Bang Cosmology. I will then discuss how we can test General Relativity using different cosmological observations, from its geometrical properties down to testing the involved propagating degrees of freedom. This analysis will also help us to classify the attempts of going beyond General Relativity together with their explicit implications.

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Abstract: In this talk, I will review recent developments on the physical implications of (extended) Bondi-Metzner-Sachs (BMS) symmetries and charges for gravity in asymptotically flat spacetimes and black hole physics.

Abstract: We experience a golden era in testing and exploring relativistic gravity. Whether it is results from gravitational wave detectors, satellite or lab experiments, radio astronomy plays an important complementary role. Here one can mention the cosmic microwave background, black hole imaging and, obviously, binary pulsars. This talk will provide an overview how these methods relate to each other, and will in particular focus on new results from the study of binary pulsars, where we can test the behaviour of strongly self-gravitating bodies with unrivalled precision. The talk will also give an outlook of what we can expect from new experiments, such as MeerKAT or the SKA.

Abstract: An empty Universe would be scale invariant, as shown by both Maxwell equations and General Relativity. The question arises on how much matter is necessary to break scale invariance in the Universe. On the basis of scale invariant models based on expressions derived by Dirac (1973), we show that scale invariant effects rapidly decline to zero for cosmological models with a density between zero and the critical one. For a density parameter Omega_m=0.3, some limited effects are remaining, which correspond to the observed accelerated expansion. Several cosmological tests are consistent, e.g. the growth of density fluctuations is boosted in the scale invariant context, a large M/L ratio is derived for clusters of galaxies, flat rotation curves are predicted in galaxies with a proper account of the radial acceleration relation (RAR).

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Abstract: Every textbook on general relativity states that light propagates along null geodesics. Although there are many senses in which this is true at sufficiently-high frequencies, it breaks down more generally. Different notions of "propagation direction" also become distinct at lower frequencies. This talk will focus on the motion "as a whole" of electromagnetic pulses with large (but not infinitely-large) frequencies. Angular momentum then affects the motion, resulting in null but non-geodesic trajectories. Precise answers depend, however, on what exactly is meant by the "pulse as a whole:" its centroid. There are many centroid definitions which appear to be reasonable, but surprisingly, some of these appear to be nowhere near the pulse itself! This turns out to be an unphysical artifact of the high-frequency approximation. Although massless spinning wavepackets appear generically in the usual approximations, no such pulses can exist non-perturbatively. High-frequency approximations break standard features of Maxwell theory, such as the fact that exact electromagnetic stress-energy tensors satisfy positive-energy conditions. It is very easy to miss this fact in practice, and doing so can result in qualitatively-incorrect conclusions regarding the motion and localization of electromagnetic waves.

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Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

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Abstract: The Hawking mass is a useful quasi-local measure for the strength of the gravitational field in initial data for the Einstein field equations of isolated gravitational systems. In this talk, I will present some recent work (joint with M. Eichmair) on so-called area-constrained Willmore surfaces in such initial data. These surfaces are area-preserving critical points of the Hawking mass and capture important physical information. We prove that the asymptotic region of an initial data set is foliated by large area-constrained Willmore spheres. We then use this asymptotic foliation to define a new notion of center of mass and study its properties compared to established notions of center of mass.

Abstract: In 1990, based on numerical and formal asymptotic analysis, Ori and Piran predicted the existence of self-similar spacetimes, called relativistic Larson-Penston solutions, that can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data, and solve the radially symmetric Einstein-Euler system with sufficiently small sound speed. I will explain a rigorous mathematical construction of such spacetimes. Joint work with Yan Guo and Juhi Jang.

Abstract: In this talk I will discuss the relation between Friedrich’s description of spatial infinity and alternative formulations by Ashtekar-Hansen and Ashtekar-Romano. Moreover, I will show how Friedrich’s framework can be used to relate a number of objects defined at null infinity to data on a Cauchy surface. Particular attention will be given to the so-called BMS charges associated to supertranslations in the case of linear fields and the case of the full non-linear GR. Writing the asymptotic charges in terms of initial data allows to establish, in a natural way, the correspondence between charges at future and past null infinity without the need of introduced an ad hoc “antipodal identification”. Moreover, it allows to clarify the required regularity of the solutions for the charges to be well defined and express these regularity requirements in terms of freely specifiable data. This is work in collaboration with Mariem Magdy Ali Mohammed.

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Abstract: The asymptotic structure of Einstein's theory at spatial infinity in five spacetime dimensions will be described, following the Hamiltonian approach. The structure of the infinite-dimensional nonlinear symmetry algebra that emerges, as well as some key (somewhat unusual) features of the charges, will in particular be addressed.

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Abstract: In this seminar, I derive McFarlane's formula for the Thomas Angle appearing in boost o boost = boost o rotation using Clifford Algebra. To do this, I first remind how to generate boosts and rotations from reflections. The composition of the latter becomes particularly easy using Clifford(-Dirac) algebra. Time permitting, I will illustrate the geometry of the situation in relativistic velocity space = hyperbolic 3-space, allowing to identify the Thomas angle with the defect of a geodesic triangle in that space.

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Abstract: This talk will be based on results from joint work with Piotr Bizoń and Bradley Cownden (https://arxiv.org/abs/2112.11249).

Abstract: In quantum physics an ideal clock can be modelled as a composite particle whose internal states ‘measure' proper time along the the particle's trajectory. However, quantum particles do do not follow classical trajectories due to Heisenberg Uncertainty Principle (HUP) for position and momentum. A question then arises what are the states of quantum clocks that follow semi-classical paths? In textbooks quantum mechanics, semiclassical states of quantum particles are the well-known Gaussian states derived from minimising the HUP. I will show that for quantum clocks semi-classically propagating states are not Gaussian but a new class of quantum states that are derived from a new uncertainty inequality — for configuration space rather than for phase space variables. I will also discuss some key properties of these states such as the inherent non-separability of their internal and external degrees of freedom, Lorentz covariance, and their relevance for experiments aimed at testing the limits of quantum theory.
Key reference Composite particles with minimum uncertainty in spacetime Phys. Rev. Research 3, 013049 (2021)

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Abstract: Infrared observations of the star cluster at the heart of our galaxy revealed the existence of a massive compact object (in best agreement with a black hole) of 4.2 million solar masses in coincident location with the radio source Sagittarius A*. The enormous efforts to confirm this have been recognised by the 2020 Nobel prize in Physics. The corresponding results demonstrate the utility of the galactic centre as a unique laboratory for relativistic astrophysics and testing relativity. In particular, the precise astrometric and spectroscopic tracking of the orbit of the star S2 allowed the observation of two prominent relativistic effects. The relativistic redshift could be observed during the last pericentre passage in 2018. The relativistic (Schwarzschild) precession of the star's orbit could be measured in 2020.
The same study also improved the 1σ upper bound on a possibly present dark continuous extended mass distribution (e.g. faint stars, stellar remnants, stellar mass black holes, or dark matter) within the orbit of S2 to ∼ 4000 solar masses. The secular (i.e. net) effect of an extended mass onto a stellar orbit is known as mass precession, and it runs counter to the Schwarzschild precession. Constraining or detecting an extended mass is not only of interest to study what is hidden in the immediate surroundings of the black hole in its own right, but also as a perturbing effect for the goal of detecting relativistic precessions (Schwarzschild, Lense-Thirring).
In my talk I will give an update on the current knowledge about the possible presence of an extended mass around Sagitarius A* by presenting the results of two recent works:

• My et al. recent theoretical and mock-data study on the impact of an extended mass on the orbit of S2. https://doi.org/10.1051/0004-6361/202142114 (first author)

• The latest observational constraints by the VLTI/GRAVITY Consortium, thanks to new data of more stars gathered in 2021 and to improved systematics. https://doi.org/10.1051/0004-6361/202142465 (corresponding author)

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Abstract: A curious fact about indistinguishable quantum particles is that there are only two types of statistics: bosonic and fermionic. The question of why only these two types of particles are admissible is usually solved via the discrete exchange symmetry of their associated quantum states. Within this approach, one proceeds naturally with the construction of (anti)symmetric wave functions and the corresponding Fock space. In this talk, I will present an alternative, operational approach in which the Fock space is postulated from the beginning. I will show that the unitary evolution of non-interacting particles is compatible with the Fock space structure only in certain cases. More precisely, I will show that the representations of the unitary group associated with the non-interacting model are classified according to the type of particle statistics. We have found the standard bosonic and fermionic representations, but also infinite classes of new types of particle statistics that (at least to our knowledge) have not previously appeared in the literature. Although a valid mathematical solution to the problem, the physical background of these anomalous statistics remains to be clarified.

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Abstract: In this work, I will present recent work on high-frequency solutions to the Einstein vacuum equations. From a physical point of view, these solutions model high-frequency gravitational waves and describe how waves travel on a fixed background metric. As noted in 1969 by Choquet-Bruhat, a wave has an effect on the background on which it travels. This is the so called backreaction phenomenon, which is also at the heart of the Burnett conjecture (stated in 1989). This conjecture adresses the lack of compactness of the family of vacuum spacetimes, for a sufficiently weak topology allowing in the limit non-trivial contribution to the matter side of the Einstein vacuum equations. The goal of my talk is to show how one can tackle those questions from the Cauchy problem in general relativity and what are the PDE challenges encountered. More precisely, after reviewing the literature on high-frequency gravitational waves and on the Burnett conjecture, I will present my work on a toy model. I will then conclude my talk by sketching the proof of the local existence in harmonic gauge of high-frequency gravitational waves.

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Abstract: I will present a geometric characterization of all possible 4-dimensional real analytic vacuum spacetimes near non-degenerate Killing horizons. This result applies in particular to bifurcate horizons (e.g. black hole event horizons) and non-degenerate compact Cauchy horizons in real analytic vacuum spacetimes, since classical results of Hawking and Moncrief-Isenberg (and recent generalizations thereof) show that such horizons are non-degenerate Killing horizons. This is joint work with Klaus Kröncke.

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Abstract: I will describe various approaches to.and results on, the asymptotics of spacetimes, or initial data sets, which are asymptotically flat at spatial infinity in 3+1 dimensions, and in higher dimensions.
Based on joint work with Peter Cameron

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Abstract: This talk describes how the Barbero--Immirzi parameter deforms the SL(2,R) symmetries on a null surface boundary. Our starting point is the definition of the action and its boundary terms. We introduce the covariant phase space and explain how the Holst term alters the symmetries on a null surface. This alteration only affects the algebra of the edge modes on a cross-section of the null surface boundar, whereas the algebra of the radiative modes is unchanged by the addition of the Barbero--Immirzi parameter. To compute the Poisson brackets explicitly, we work on an auxiliary phase space, where the SL(2,R) symmetries of the boundary fields are manifest. The physical phase space is obtained by imposing both first-class and second-class constraints. All gauge generators are at most quadratic in terms of the fundamental SL(2,R) variables. Finally, we discuss various strategies to quantise the system.
The talk is based on the paper: https://arxiv.org/abs/2104.05803

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Abstract: I will describe a construction of asymptotically locally hyperbolic metrics with negative scalar curvature (i.e., vacuum zero-extrinsic-curvature general relativistic initial data sets) with negative total mass. Based on joint work with Raphaela Wutte and Erwann Delay.

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Abstract: Black holes have been accepted as thermodynamic systems ever since Hawking’s discovery of black hole radiation. The thermodynamic phase space of AdS black holes has been extended to include a P-V term in [1]. By studying the equation of state of AdS black holes in this extended phase space, many interesting phase transitions were found; a prominent example is the Van der Waals like small-to-large phase transition of charged AdS black holes which takes place below a critical pressure [2]. Recently, Visser reconsidered the situation in the context of holography [3]. While the natural unit G=1 was kept in previous studies, Visser argued that considering variations of G is necessary to achieve a duality between the bulk and boundary thermodynamic first laws. I will briefly review his argument, and rewrite the bulk first law in a new form containing both variations of P and C, the central charge of the dual CFT. This leads to a new understanding of the Van der Waals behaviour of charged AdS black holes, where the phase changes are now governed by C instead of P.
[1] D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011, [0904.2765].
[2] D. Kubiznak and R. B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033, [1205.0559].
[3] M. Visser, Holographic Thermodynamics Requires a Chemical Potential for Color, [2101.04145].

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Abstract: : In this talk, our recent proof of the Hawking-Penrose singularity theorem, as well as its generalization due to Galloway and Senovilla, to C^1-Lorentzian metrics will be discussed. We will start by presenting tensor distributions of finite order as the proper setting for defining curvature conditions for C^1-metrics, and then go on to address geodesic branching, a phenomenon that can occur in this regularity since the geodesic equation is no longer uniquely solvable.
Finally, we give an outline of the proof of the main result by means of regularized metrics, using refined versions of the Riccati comparison techniques that were used in the proof of the C^{1,1} Hawking-Penrose theorem.

Abstract: In this talk we describe a new monotonicity formula holding along the level sets of the Green's function of an asymptotically flat 3-manifold with nonnegative scalar curvature. Using such a formula, we obtain a simple proof of the celebrated positive mass theorem. In the same context, and for 1<p<3, a Geroch-type calculation is performed along the level sets of p-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality in some case studies. The results are obtained in collaboration with V. Agostiniani and F. Oronzio.

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Abstract: In 2012, Maliborski [1] gave numerical evidence for the non-linear instability of a portion of (3+1) dimensional Minkowski spacetime enclosed inside a timelike worldtube ℝ⨉B³ with a perfectly reflecting wall under arbitrarily small perturbations. The numerical evidence was corroborated by a weakly non-linear perturbation analysis which revealed the existence of secular terms, i.e. terms that grow without bounds, in the perturbative series, which were conjectured to be progenitors of a resonant mode mixing which causes the transfer of energy from lower to higher modes. In light of this analysis, we derive the resonant approximation for this system using 1) the method of multiple scales and 2) the renormalization group method [2] with the aim of resumming the secular terms in the perturbative series in order to get a description of the relevant dynamics that is valid at long times. We solve the resulting system of coupled first order differential equations, called the resonant system, numerically and illustrate in detail its solution. Furthermore, we analyze the mode amplitude spectrum using the analyticity strip method [3]. We find that the amplitude spectrum evolves to a power law in finite time, which corresponds to the solution of the resonant system becoming singular. Moreover, we find that the value for the power law exponent determined in our analysis is in agreement with the corresponding value observed by Maliborski [1] in the fully non-linear evolution of the system. We interpret these findings as corroborating the results regarding the instability of flat space enclosed in a cavity given in [1].

[1] M. Maliborski, „Instability of flat space enclosed in a cavity“, Phys. Rev. Lett. 109, 221101 (2012).
[2] L. Y. Chen, N. Goldenfeld, and Y. Oono, „Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory“, Phys. Rev. E 54, 376 (1996)
[3] C. Sulem, P.L. Sulem, and H. Frisch, „Tracing complex singularities with spectral methods“, J. Comput. Phys. 50, 138 (1983).

Abstract: A still much debated question in the field of relativistic quantum information is whether entanglement and the degree of violation of Bell's inequalities are (Lorentz) frame independent for massive relativistic particles. Central to this question is the effect that spin gets entangled with the momentum at relativistic velocities with respect to the laboratory frame. In my talk, I will present a quantum reference frame transformation that allows us to transform a particle to the rest state even if it is in a superposition of relativistic momenta. In this way, we can first go to the rest state of the particle, perform mentally the spin measurements there (using the Stern-Gerlach experiment), and then return to the laboratory frame. In this way, we find the operational "relativistic spin" and show that entanglement and Bell's inequality are invariant for a pair of particles when changing the quantum reference frame.

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Abstract: We review the asymptotic initial value problem in all dimensions for the Λ>0-vacuum Einstein metrics in the Fefferman-Graham picture. We give a geometric definition of the initial data in the conformally flat $\mathscr{I}$ case and a Killing initial data equation for the analytic data case. We use these results to characterize the Kerr-de Sitter family of metrics in all dimensions in terms of asymptotic initial data, which are given by a conformally flat boundary metric γ and a TT tensor canonically constructed from a particular conformal Killing vector (CKV) ξ_{K dS} of γ. The data naturally generalize for an arbitrary CKV ξ, extending the definition of the Kerr-de Sitter-like class (with conformally flat $\mathscr{I}$) to arbitrary dimensions by means of asymptotic data. We prove that each metric in the class corresponds to a (conformal) class of CKVs, i.e. the set generated from ξ by local conformal transformations of γ. This fact endows the space of metrics with a structure of limits, which we analyze. This allows us to make explicit all the metrics in the class and identify them with the set of Λ>0-vacuum and conformally extendable Kerr-Schild metrics with an additional decay condition at $\mathscr{I}$.

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Abstract: In this talk an overview of the theory of general relativistic elasticity in a gravitational wave background will be presented. The main topic of interest is the response of elastic materials or bodies to the incidence of a gravitational wave in the transverse-traceless gauge. Starting from the concept of an action principle, the primary object in question is the energy-momentum or stress-energy tensor T_μν coming from a Lagrangian field theory. The vanishing divergence of T_μν then leads to a wave equation, where the gravitational wave enters through the boundary conditions (as an effective force). A one-dimensional example for an elastic material in a gravitational wave background is provided, where an exact solution is obtained.

Abstract: Smooth compact totally geodesic null hypersurfaces (horizons) arise naturally as Cauchy horizons for partial Cauchy hypersurfaces.
Here I outline a recent proof that if they admit an incomplete generator (non-degenerate) then the surface gravity can be normalized to a non-zero constant.The proof is, in its most technical part, independent of the approach of Isenberg-Moncrief and Bustamante-Reiris. Also the result holds just under the dominant energy condition, i.e. no vacuum assumption is required. If time permits, I shall also outline the proof that they are actually Cauchy horizons bounded on one-side by a region of chronology violation. (This is joint work with Sebastian Gurriaran, ENS Paris-Saclay)

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Abstract: The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. By considering the WKB approximation for Maxwell's equations, I will briefly present the main steps of a covariant derivation of the polarization-dependent ray equations describing the gravitational spin Hall effect of light. I will also discuss the relation of these equations with the well-known MPD equations, as well as the observer dependence of the position of massless spinning particles.

Abstract: Due to their nonlinear nature, the Einstein equations are not closed under weak convergence: failure of compactness, due to oscillations and concentrations, produces an excess energy momentum tensor. In 1989, Burnett conjectured that, for vacuum sequences with high-frequency oscillations, the matter produced in this limit is captured by the Einstein-massless Vlasov model.
In this talk, we give a proof of Burnett's conjecture under some gauge and symmetry assumptions, improving previous work by Huneau—Luk from 2019. Our methods are more general, and apply to oscillating sequences of solutions to the wave maps equation in (1+2)-dimensions.
This is joint work with André Guerra (Institute for Advanced Study).

Abstract: Physics has two wonderful theories, relativity and quantum theory, but their marriage seems troublesome. In this talk I will focus on one of the most striking quantum phenomenon, entanglement, which is considered to be, e.g., the essential ingredient in the better performance of the formidable quantum computers compared with classical ones or may become a way to detect and monitor cancer. In particular, I will raise the question what happens if the entanglement is observed by a boosted observer? Obviously, here two very different ontologies meet and I will discuss how they come together from the quantum information theoretic point of view and which non-trivial and counter-intuitive effects arise due to geometry.

Abstract: Some applications require non-Riemannian spacetimes, such as Carrollian or Galilean spacetimes. They describe, respectively, ultra- and non-relativistic limits of gravity. In my talk I construct the Newton-Cartan version of two-dimensional dilaton gravity, which plays essentially the same role for Newton-Cartan gravity as generic dilaton gravity does for Riemann-Cartan gravity.
LINK: https://arxiv.org/abs/2011.13870

Abstract: I give an informal overview of quantum extremal surfaces defined by Engelhardt and Wall, addressing the following questions: What are extremal surfaces? Why do we need them? Why do we need quantum extremal surfaces? What are they? Why is this definition relevant?
Which applications do they have?

Abstract: The mathematical problem of stability of black hole solutions of Einstein’s equations is important to establish the astrophysical significance of these solutions. The problem concerns the stability of the Kerr(-Newman) family of solutions of the Einstein(-Maxwell) equations. In terms of mathematical technique, an important obstacle is that the energy of waves propagating through such spacetimes is not necessarily positive-definite due to the existence of the ergoregion for non-zero angular momentum.
In this talk, we shall discuss the proof that there exists an energy functional for axially symmetric linear perturbations of Kerr-Newman that is positive-definite and strictly conserved. The proof is based on a Hamiltonian approach to the Einstein equations and holds for the full sub-extremal range. This is joint work with Vincent Moncrief.

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Abstract: In this talk we introduce the characteristic gluing problem for the Einstein vacuum equations. We show that the obstructions to characteristic gluing of spacetimes come from an infinite-dimensional space of conserved charges along null hypersurfaces. We prove that this space splits into an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges. We identify the 10 gauge-invariant charges to be related to the energy, linear momentum, angular momentum and center-of-mass of the spacetime. Based on this identification, we explain how to characteristically glue a given spacetime to a suitably chosen Kerr spacetime. As corollary we get an alternative proof of the Corvino-Schoen spacelike gluing to Kerr. Moreover, we apply our characteristic gluing method to localise characteristic initial data along null hypersurfaces. In particular, this subsequently yields a new proof of the Carlotto-Schoen spacelike localization where our method yields no loss of decay, thus resolving an open problem. We also outline further applications. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Princeton).

Abstract: This talk is intended to give a comprehensive primer on Hong-Ou-Mandel (HOM) Interference, which is a quantum mechanical effect useful in quantifying indistinguishability of photons. In particular, it can be employed to measure the decoherence generated in a system (i.e. the interaction with its surroundings). This enables a setup which can encode general relativistic effects into quantum-interference experiments, potentially leading to an observation of quantized electromagnetic fields in the context of general relativity.

Abstract: I will discuss recent work with M. Dafermos, I. Rodnianski and M. Taylor proving the full finite codimension asymptotic stability of the Schwarzschild family of black holes in the exterior of the black hole region. The proof is expressed entirely in physical space and based on our previous understanding of linear stability of the Schwarzschild family in a double null gauge.

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Abstract: The introduction of the Bondi-Sachs formulation was a foundational breakthrough in the understanding of gravitational waves "at" infinity, and to this day formulations of this type are routinely used in numerical relativity for a variety of purposes. In my talk I will discuss recent work in collaboration with Thanasis Giannakopoulos and Miguel Zilhao concerning the local well-posedness of the characteristic initial boundary value problem employing such formulations. Surprisingly, we find that these systems are only weakly hyperbolic, meaning that text-book theorems on well-posedness cannot be straightforwardly applied. Finally I will discuss the consequence of this finding in the numerical setting by using simple toy models.

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Abstract: I will introduce the celebrated Kerr black hole stability conjecture according to which the Kerr family of metrics are stable as solutions to the Einstein vacuum equations of general relativity. I will then focus on recent developments concerning this problem.

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Abstract: I will present some of the results from the recent Dark Energy Survey year 3 analysis. In particular, I will focus on the cosmological results paper:
https://www.darkenergysurvey.org/wp-content/uploads/2021/05/desy3_3x2_results.pdf
where they constrain parameters such as the matter density Omega_m, dark energy equation-of-state parameter w, and the clustering amplitude S_8.
More papers from this release can be found here:
https://www.darkenergysurvey.org/des-year-3-cosmology-results-papers/

Abstract: Bodies floating in still water are subject to the laws of rigid body mechanics combined with Archimedes' principle. We write down the equations governing their dynamics. These equations take the form of a Hamiltonian system similar to, but richer in structure than, the well-known heavy top. The sometimes surprising equilibrium configurations of floating bodies have attracted interest from the times of Archimedes up until today. The stability properties of equilibria have essentially been known since the 18th century and extensively used in naval architecture and by glaciologists studying icebergs. We give a precise statement of these stability criteria and an elementary proof of nonlinear stability under time evolution.

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Abstract: In this talk we will investigate the past dynamics of cosmological solutions to Einstein's equations, containing a Big Bang singularity. More precisely, we will focus on the classical generalized Kasner examples. The celebrated ``singularity'' theorem of Hawking states that the past of sufficiently small perturbations of such solutions is causally geodesically incomplete. However, it is not in general known whether such a degeneracy is related to the formation of a curvature singularity. In many cases, unstable dynamics are predicted, which adds to the difficulty of the problem. We will discuss a recent joint work with I. Rodnianski and J. Speck that classifies the behavior of perturbed solutions in the so-called subcritical regime.

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Abstract: High energy laser beams and particle beams, such as the one of the Large Hadron Collider (LHC) at CERN, can be used as lab-scale, relativistic sources of gravitational fields.We present a study of the creation and possibility of detection of oscillating gravitational fields from lab-scale, relativistic sources. Lab-based sources allow for signal frequencies much higher and far narrower in bandwidth than what most celestial sources produce. In addition, by modulating the source beams, the source frequency can be adjusted over a very broad range. In this talk we show an analysis of the gravitational field produced by these sources and the responses of a variety of detectors, with the outlook that an adapted version of a recently experimentally demonstrated high-Q monolithic pendulum might be able to detect the gravitational signal produced by the planned high-luminosity upgrade of the LHC.

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Abstract: Geometrical optics consists of approximating the evolution of an electromagnetic wave, solution to Maxwell’s equations, by ray equations. In the limit of infinite frequencies, the rays have the usual semi-classical interpretation of being the paths of photons, null geodesics. At high but finite frequencies, corrections to these rays are expected. For light propagating in a medium, these corrections have been observed. In quantum mechanics, corrections in the context of adiabatic perturbations theory are well-studied. Wigner functions belong to the tools commonly used to capture them. In this talk, I will present a covariant version of Wigner-Weyl calculus which can, at least formally, be used in relativity. Corrections to geometrical optics can then be calculated, and one recovers results previously obtained by Oancea, et al., and Andersson, et al.. The effective ray equations can be recast as massless MPD equations, with a specific supplementary condition.

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Abstract: The outstanding issue of a non-singular extension of the Kerr-NUT-(anti) de Sitter solutions to Einstein's equations is solved completely. The Misner's method of obtaining the extension for Taub-NUT spacetime is generalized in a non-singular manner. The Killing vectors that define non-singular spaces of non-null orbits are derived and applied. The global structure of spacetime is discussed. The non-singular conformal geometry of the null infinities is derived. The Killing horizons are present.

Abstract: In this talk, I will discuss the recent work with David Fajman on stability of a subclass of the negatively curved FLRW models, the so-called Milne universe, in the set of the solutions to the Einstein-Vlasov-Maxwell system. The Milne universe is a vacuum non-accelerating expanding cosmological model for which some stability results are known. After reviewing the previous results on the stability of this model, I will describe the ideas of the proof and focus on the subtleties of the Einstein-Vlasov-Maxwell case that arise from the coupling of the two matter fields which again couple to the Einstein equations in the so-called CMCSH gauge. This work provides the first stability result for the Einstein-Vlasov-Maxwell system and it generalizes the results of Andersson-Moncrief, Andersson-Fajman, and Branding-Fajman-Kröncke in 3+1 dimensions.

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Abstract: In this talk, I will discuss recent results concerning the global stability to the future of solutions to the relativistic Euler equation on expanding cosmological spacetimes. The first part of the talk will be a review focusing on what is known about the stability and instability of relativistic fluids on cosmological backgrounds. In the second part of the talk, I will discuss new stability results for relativistic fluids with a linear equation of state p = K_ρ on FLRW spacetimes where the equation of state parameter value K satisfies ¹/₃ < Κ < ¹/₂ . This new stability result is of particular interest because it was previously conjectured that instabilities should develop for the parameter values ¹/₃ < K < 1 . Time permitting, I will conclude the talk with a discussion of future projects and areas for further research.

Abstract: Testing gravity with genuine quantum systems is on the agenda of many experimental groups worldwide. Such programmes presuppose a well defined scheme according to which the coupling of quantum matter to the classical gravitational field is determined. Such schemes do not exist. Ideally, they should be complete (i.e. account for all terms, say in a given PN-order) and generally applicable (i.e. without a priori restrictions on the quantum states the matter is assuming). But what are the hard principles on which such a scheme can be based?
In the first part I will report on some recent work in which the Hamiltonian of an electromagnetically bound 2-particle "atom” in a static Eddington–Robertson parametrised post-Newtonian gravitational field is “derived” to order (1/c)-squared. In the second part will I turn to the Schrödinger-Newton equation as semiclassical model for gravitational self-coupling of quantum systems.

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Abstract: I will motivate the idea of quantum fields on a classical spacetime as a fundamental theory, giving rise to dynamics governed by the nonlinear Schrödinger-Newton equation in the nonrelativistic limit. I discuss the issue that arises from this nonlinear evolution regarding causality and how it may be avoided in a model that encompasses a mechanism for objective wave function collapse.
I will further discuss gravity-induced entanglement as a proxy for the quantisation of gravity, and argue that experimental tests of quantum versus semiclassical gravity through entanglement generation are strongly constrained by acceleration noise.

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Abstract: Motivated by a possible quantum gravity construction, Penrose has shown that, despite being asymptotically flat, there is an inconsistency between the causal structure at infinity of Schwarzschild and Minkowski spacetimes. However, the proof of this inconsistency is specific to 4 spacetime dimensions. In this talk I will discuss how this result extends to higher (and lower) dimensions. More generally, I will consider examples of how the causal structure of asymptotically flat spacetimes are affected by dimension and by the presence of mass (both positive and negative). I will then show how these ideas can be used to prove a higher dimensional extension of the positive mass theorem of Penrose, Sorkin and Woolgar.

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Abstract: Motivated by the concept of mass for asymptotically hyperbolic metrics, we study invariants of pairs of metrics that are asymptotic to a certain order. We work in the setting of conformally compact metrics on arbitrary manifolds with boundary (at infinity). We need all metrics to be asymptotically hyperbolic in a very weak sense and then look at a class of metrics that are asymptotic to an appropriate higher order. This in particular ensures that all the metrics in the class induce the same conformal infinity on the boundary, and we construct local invariants as tractors for this conformal structure.
In the general setting (no restriction on the topology or further restrictions on the class) we obtain local invariants for pairs of metrics which satisfy a cocycle condition and remain unchanged if one of the factors is pulled back along a diffeomorphism that is asymptotic to the identity. In the special case that of the closed ball and a class of metrics containing a hyperbolic metric, we recover the classical mass of metrics in the class via an integral (in an appropriate sense) of our invariant.

Abstract: If a quantum particle exists in a superposition state of being at two different spatial positions, can we also consider the gravitational field to be superposed? What does this mean in terms of the spacetime geometry? There is no way of answering these questions currently, as the answers can only be provided by experiments which we do not yet have. However, advances in experimental techniques have led to various proposals which propose to prepare masses in spatial superpositions. In this talk, I will make use of one of these proposals utilizing optomechanical techniques in achieving the superposition. I will study what the observable effects are if the answer to the first question were true. More specifically, I will demonstrate what the effects on the interference visibility (a quantity measurable from the experiment) are if we describe the interaction between two superposed masses using the canonical Schrodinger evolution. I will also show that this interaction leads to quantum entanglement between the two masses. This talk is based on the paper Phys. Rev. A 98, 043811 (2018), arXiv: 1806.06008.

Abstract: Vanishing of the Fefferman-Graham obstruction tensor was proposed by Anderson and Chrusciel as a tool for studying asymptotically simple solutions to Einstein's equations. It is a conformally covariant equation and a stronger condition: every lambda-vacuum solution in any even dimension has vanishing Fefferman-Graham tensor. The equation is an alternative for known Friedrich's construction of conformal version of Einstein's equations. This approach will work if one can show that the equation is hyperbolic. I will discuss the proof in my talk.

Abstract: We discuss the problem of the classification of static vacuum spacetimes with negative cosmological constant. One of the few known results on the subject is a uniqueness theorem for Kottler solutions with nonpositive mass, proved by Lee and Neves through the employment of a Penrose inequality for asymptotically locally hyperbolic manifolds. We will discuss an alternative more elementary proof of this uniqueness result, which has the added benefit of easily generalizing to degenerate horizons. Time permitting, we will then show how similar techniques can be applied in other frameworks, such as in the study of the positive cosmological constant case.

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Abstract: Beyond huge leaps in the exploration of extreme astrophysical systems Earth-bound experiments have continuously been refined for sensing gravity phenomena on laboratory scales i.e. in the low energy limit. A yet unexplored frontier is the regime of microscopic source masses, which provides a natural path towards exploring the quantum nature of gravity. We recently demonstrated gravitational coupling between two ≈90 mg gold spheres with a systematic accuracy of 4^-11m/s² and a statistical precision of 4^-12m/s² in a miniaturized torsion balance experiment. We expect further improvements of the setup to enable the isolation of gravity as a coupling force for objects well below the Planck mass in the next iteration. These top down efforts strive to ultimately culminate in a purely gravitational coupling of quantum objects.

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Abstract: In this talk I will discuss a new spinorial strategy for the construction of geometric inequalities involving the ADM mass of black hole systems in General Relativity. This approach is based on a second order elliptic equation (the approximate twistor equation) for a valence 1 Weyl spinor. This has the advantage over other spinorial approaches to the construction of geometric inequalities based on the Sen-Witten-Dirac equation that it allows to specify boundary conditions for the two components of the spinor. This greater control on the boundary data has the potential of giving rise to new geometric inequalities involving the mass. In particular, I will show that the mass is bounded from below by an integral functional over a marginally outer trapped surface (MOTS) which depends on a freely specifiable valence 1 spinor. From this main inequality, by choosing the free data in an appropriate way, one obtains a new nontrivial bounds of the mass in terms of the inner expansion of the MOTS. The analysis makes use of a new formalism for the 1+1+2 decomposition of spinorial equations. This work was done in collaboration with J. Kopinski (Warsaw).

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Abstract: An intriguing open problem in general relativity is the question as to whether stationary equilibrium configurations with clearly separated bodies can exist. Due to the nonlinear effect of the spin-spin repulsion of rotating objects, and perhaps by considering charged objects with an additional electromagnetic repulsion, it remains a possibility that such unusual configurations do exist. An important example of an n-body system is a (hypothetical) equilibrium configuration with n aligned rotating and possibly charged black holes. By studying the linear matrix problem that is equivalent to the Einstein (-Maxwell) equations for axixymmetric and stationary (electro) vacuum spacetimes, we obtain the most general form of the boundary data on the symmetry axis in terms of a finite number of parameters. This will be illustrated with the simplest case of one black hole in vacuum, and we briefly discuss how an electromagnetic field can be included and the discussion be extended to arbitrary n. In the simplest case n=1, this leads to a constructive uniqueness proof of the Kerr (-Newman) solution. For n=2 and vacuum, one obtains non-existence of stationary two-black-hole configurations. For n=2 with electrovacuum, and for larger n, it remains an open problem whether the well-defined finite solution families contain any physically reasonable solutions, i.e. spacetimes without naked singularities, magnetic monopoles and struts.

Abstract: Let (Σⁿ⁻¹, γ, H ) be an orientable n−1 -dimensional Riemannian manifold, H be a positive function on Σ. One of basic problems in Riemannian geometry is to ask: under what conditions is it that γ is induced by a Riemannian metric g with nonnegative scalar curvature, for example, defined on Ωⁿ, and H is the mean curvature of Σ in Ω with respect to the outward unit normal vector? Recently, M.Gromov proposed several conjectures relate to this problem. In this talk, I will discuss the relation of this problem with the positive mass theorem, and present my recent work on this which joints with Dr.Wang Wenlong, Dr.Wei Guodong，and Zhu Jintian. The talk with the same title was delivered in “Virtual Workshop on Ricci and Scalar Curvature in honor of Gromov “ in this July, I will give proofs of some results which were not given in the previous talk.
This talk is based on my recent joint paper named “Total mean curvature of the boundary and nonnegative scalar curvature fill-ins” which can be found at https://arxiv.org/pdf/2007.06756.pdf.

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Abstract: I will give a brief introduction into the equations of motion in Kerr spacetime and discuss some features resulting from them. Concentrating on vortical null geodesics (those with negative Carter constant), I will present a way to solve the equations of motion analytically and numerically. To conclude, I will present some preliminary visualisations of such vortical null geodesics, both single trajectories as well as what an observer located far away from the black hole in the region of negative radii would see.

Abstract: In this talk, we investigate whether correspondences exist between vacuum asymptotically Anti-de Sitter spacetimes and properties of their conformal boundaries. Here, we focus primarily on the question of whether a symmetry on such a conformal boundary must be inherited by the spacetime itself. In particular, we present the first positive results in this direction for non-stationary settings, and we discuss recent developments in unique continuation theory that lead to these results.
The presentation involves joint works with Gustav Holzegel and Alex McGill (as well as work in progress with Athanasios Chatzikaleas).

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Abstract: In this talk I will present a new model for the description of a gravitating kinetic gas, by coupling the 1-particle distribution function (1PDF) of the gas directly to the gravitational field, lifted to the tangent bundle of spacetime. This procedure takes the influence of the velocity distribution of the kinetic gas particles on their gravitational field fully into account, instead of only on average, as it is the case for the Einstein-Vlasov system.
By using Finsler spacetime geometry I construct an action for the kinetic gas on the tangent bundle, which is added as matter action to a canonical Finslerian generalisation of the Einstein-Hilbert action. The invariance of the kinetic gas action under coordinate changes gives rise to a new notion of energy-momentum conservation of a kinetic gas in terms of an energy-momentum distribution tensor. The variation of the total action with respect to the spacetime geometry defining Finsler Lagrangian yields a gravitational field equation on the tangent bundle, which determines the geometry of spacetime directly from the full non-averaged 1PDF. This equation can be regarded as generalisation of the Einstein-Vlasov system, which takes all features of the kinetic gas into account.

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Abstract: In this talk, I will discuss how gravitational waves of low frequency perturb the electromagnetic modes in step-index optical fibres. After reviewing previous analyses of non-inertial effects in fibre-optic waveguides, I will discuss how weak gravitational waves alter Maxwell’s equations for linear dielectrics. Solving these equations perturbatively (with boundary conditions appropriate to describe single-mode optical fibres) leads to explicit results for the first order correction of the fibre modes. In particular, I will discuss the perturbation of the phase and polarisation of light in such waveguides.

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Abstract: An introduction to non-perturbative approaches to quantum gravity will be given. The talk will focus on the quasi-local approach and explain the distinction between observables, symmetries and gauge symmetries in the context of classical and quantum general relativity.

Abstract: Given a solution of the Einstein equations a fundamental question is whether one can extend the solution or whether the solution is maximal. If the solution is inextendible in a certain regularity class due to the geometry becoming singular, a further question is whether the strength of the singularity is such that it terminates classical time-evolution.
In this talk we give an overview of low-regularity inextendibility results for Lorentzian manifolds and then focus on recent results showing the locally Lipschitz inextendibility of FLRW models with particle horizons and spherically symmetric weak null singularities. The latter in particular apply to the spherically symmetric spacetimes constructed by Luk and Oh, improving their C²-formulation of strong cosmic censorship to a locally Lipschitz formulation.

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Abstract: In this talk, I will discuss my work on a direct rigorous mathematical proof of the Gregory--Laflamme instability for the five-dimensional Schwarzschild black string (https://arxiv.org/abs/2007.08441). This is a mode instability at the level of the linearised vacuum Einstein equation. Under a choice of ansatz for the perturbation and a gauge choice, the linearised vacuum Einstein equation reduces to an ODE problem for a single function. In this work, a suitable rescaling and change of variables is applied which casts the ODE into a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution which has admissible behaviour at the future event horizon and spacelike infinity. After the addition of a pure gauge solution, this gives rise to a regular exponentially growing mode solution of the linearised vacuum Einstein equation in harmonic/transverse-traceless gauge.

Abstract: Dark matter is, alongside dark energy, one of the most elusive problems in contemporary cosmology. The cold dark matter model provides a good explanation of many phenomena of large scale structure formation. However, direct searches for the fundamental particle of this model have been to no avail, despite covering a large part of the parameter space. Many alternatives have been proposed, spanning more than fifty orders of magnitude in the corresponding particle's mass. In my talk, I will present the idea that dark matter consists of a large number of ultralight particles which can be described by a scalar field obeying the Schroedinger-Poisson equations. This model is also known as the "fuzzy dark matter" and is indistinguishable from the CDM on large cosmological sales. On galactic scales however, the effects of the wavelike nature of the scalar field become apparent and can potentially be observed. I will also show some new results demonstrating the impact of various fractions of cold and fuzzy dark matter on cosmic structures using our new AxioNyx simulation code.

Abstract: Bartnik's quasi-local mass for a compact manifold with boundary is defined by minimizing the ADM masses among admissible extensions. Among several proposed conjectures, Bartnik's stationary conjecture asserts that a minimizing initial data set must be vacuum and admit a timelike Killing vector. We make partial progress toward this conjecture by showing that a minimizing initial data set must sit in a "null dust" spacetime carrying a global Killing vector. On the other hand, we find pp-wave counterexamples to Bartnik's stationary and strict positivity conjectures in dimensions greater than 8.
In our proof, we introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability using a new infinite-dimensional family of deformation to the Einstein constraint operator. This talk is based on a joint work with Dan Lee .

Abstract: No doubt, the Equivalence Principle is at the heart of General Relativity, tested in many aspects. It is often used to discuss qualitatively the influence of gravity on physical phenomena. But can this also be made more precise? In this elementary talk I compare clock rates, frequency shifts, light deflection and even time delay in simple static spacetimes to the analog phenomena seen by accelerated observers in Minkowski space.

Abstract: The almost splitting theorem of Cheeger-Colding is generalized to the setting of almost nonnegative m-Bakry-Emery Ricci curvature, in which is positive and the associated vector field is not necessarily required to be the gradient of a function. In this context it is shown that with a diameter upper bound and volume lower bound the fundamental group of such manifolds is almost abelian. Furthermore, extensions of well-known results concerning Ricci curvature lower bounds are given for generalized m-Bakry-Emery Ricci curvature. This analysis is then applied to stationary vacuum black holes in higher dimensions to find that low temperature horizons must have limited topology, similar to the restrictions exhibited by (extreme) horizons of zero temperature. Lastly, applications to cosmology are also described. Here restrictions are obtained on the list of possible topologies of the universe. This is joint work with Greg Galloway and Eric Woolgar.

Abstract: I'll discuss some new tools for studying the scalar curvature of 3-dimensional manifolds, exploiting a relationship between scalar curvature and the topology of level sets of harmonic functions and S^1-valued harmonic maps. These methods share features with the well-known minimal surface and inverse mean curvature flow techniques, while yielding some estimates reminiscent of those arising from Dirac operator methods. We'll describe applications to the study of the Thurston norm of closed 3-manifolds, and the ADM mass of asymptotically flat 3-manifolds. (Based in part on joint work with Hugh Bray, Demetre Kazaras, and Marcus Khuri.)

Abstract: (tba)

Abstract: We will discuss the method of Maliborski-Rostworowski initially developed for the Einstein-Klein-Gordon system within spherical symmetry and used to provide numerical evidence for the existence of time periodic solutions. Then, we will comment on how one can use this method to rigorously prove the existence of time periodic solutions for simple models which "capture" the instability of the Anti-de-Sitter solution to the Einstein equations.

Abstract: Spacetimes with compact directions, which have special holonomy such as Calabi-Yau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, non-linear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This talk is based on joint work with Lars Andersson, Pieter Blue and Shing-Tung Yau.

Abstract: Using the deep connection between gravity and thermodynamics, we derived the modified Friedmann equations and Newton’s law of gravity based on Tsallis entropy. We show that the cosmological model based on non-extensive Tsallis entropy can explain the late time accelerated expansion and flat galactic rotation curves without needing dark energy and dark matter.

Abstract: I'll discuss some new tools for studying the scalar curvature of 3-dimensional manifolds, exploiting a relationship between scalar curvature and the topology of level sets of harmonic functions and S^1-valued harmonic maps. These methods share features with the well-known minimal surface and inverse mean curvature flow techniques, while yielding some estimates reminiscent of those arising from Dirac operator methods. We'll describe applications to the study of the Thurston norm of closed 3-manifolds, and the ADM mass of asymptotically flat 3-manifolds. (Based in part on joint work with Hugh Bray, Demetre Kazaras, and Marcus Khuri.)

Abstract: The standard perturbation series used to compute the trajectories of light rays in weak, monochromatic, plane gravitational wave backgrounds is valid for short times only due to the presence of secular terms. However, one can extend the range of validity of the perturbative series using the method of multiple scales. The such obtained trajectories show that light rays experience a permanent shift from the unperturbed straight lines, resulting in a displacement of the beam by a distance of the order of the wavelength of the gravitational wave.

Abstract: I will present how one may derive the Einstein-Vlasov equations for collisionless matter from a variational principle. The main idea is to consider the Einstein-Vlasov matter as an analog of pressureless dust, but moving in the tangent bundle over the spacetime instead of the spacetime itself.

Abstract: The Kasner solutions are explicit solutions to the Einstein vacuum equations with a spacelike singularity. I will present a recent construction of a class of Kasner-like singularities without any symmetry and analyticity assumptions. The construction in particular relies on a new energy estimate for the second fundamental form of solutions to the Einstein vacuum equations in a synchronized coordinate system. This is a joint work with Grigorios Fournodavlos.

Abstract: I will present a method of constructing solutions to the Einstein-Vlasov system under stationarity and spherical symmetry assumptions. These solutions have the property that the spatial support of the matter is a finite, spherically symmetric shell located away from the black hole . To this end, I will start by reviewing some of the progress made in the context of solutions to the Einstein-Vlasov system. Then, I will explain how the study of trapped timelike geodesics in a perturbed Schwarzschild spacetime allowed us to provide one-parameter family of solutions.

Abstract: A big open question in cosmology is to understand the initial conditions of our universe. It remains unclear to what extent consistency requirements stemming from quantum gravity will fix these conditions, and to what extent additional input from a separate theory of initial conditions will be required. Most such additional theories have been formulated in the context of the path integral approach to gravity, since it allows for a clear specification of boundary conditions. I will review progress in evaluating gravitational path integrals, and the implications for the well-known no-boundary and tunnelling proposals.

Abstract: The talk gives an overview of the application of abstract operator theoretic methods, from the area of semigroups of operators, to evolution equations, in particular, of the hyperbolic type. For the case of time-dependent linear and quasi-linear evolution equations, the talk focuses on applications of the late Tosio Kato’s most recent theorems. Complete details are given in the speaker’s book, ”Beyond partial differential equations: On linear and quasi-linear abstract hyperbolic evolution equations”, Springer Lecture Notes in Mathematics, LNM 1898, Springer: Berlin, 2007

Abstract: With the advent of the first picture of a black hole taken by the Event Horizon Telescop collaboration we entered a new age of black hole research. In my talk I will ask,how much information an observer can hope to retrieve, at best, from such observations. First I will introduce the concept of the shadow of a black hole and what it means for the shadows of two observers to be degenerate. I will then show that no continuous degenerations exist between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass and hence all parameters can in principle be extracted from an observation.

Abstract: We will consider in this talk the Einstein-Lichnerowicz system of equations. It originates in General Relativity as a way to determine initial-data sets for the evolution problem. This system takes the form of a strongly coupled, supercritical, nonlinear system of elliptic PDEs. We will investigate its blow-up properties and show that, in large dimensions, it possesses a non-compact family of solutions. This family of solutions will be constructed by combining toplogical methods with a finite-dimensional reduction approach; due to the non-variational structure of the system, the latter has to be carried on in strong spaces and relies of a priori blow-up estimates that we shall describe.

Abstract: I will present a parametrisation, by unconstrained tensor fields, of solutions of the linearised constraint equations on static slices of Minkowski, de Sitter, and anti de Sitter.

Abstract: The wish to "give a mass to the graviton" (or to make gravity finite range) is old and has motivations ranging from cosmology to the achievement of a theoretical challenge. After reviewing the attempts in this direction and their numerous obstacles, I will discuss recent progresses. In a second part of the talk, I will introduce some our results on the construction of a consistent partially massless graviton on curved backgrounds as well as that of a theory of multiple partially massless such fields.

Abstract: A marginally trapped surface (MTS) is a compact two-surface in spacetime such that (at least) one of the two families of orthogonally emanating null geodesics has vanishing expansion. Compared to related concepts like trapped surface, apparent horizon, etc., a MTS is the least restrictive key ingredient in results on black hole formation and -merger, as well as for singularity formation in General Relativity.
The mathematical analysis of MTSs involves differential geometry, bifurcation analysis, and elliptic theory applied to quasilinear equations, in particular Jang’s equation.
We give simple examples of spacetimes with and without MTS, quote mathematical results, prove a few simple ones, expose their role in black hole physics mentioned above, and compare with recent numerical simulations.

Abstract: In spatially homogenous cosmologies with a massive scalar field, oscillations enter the Einstein-matter system via the Klein-Gordon equation. These oscillations are generally nontrivial to control, hindering tasks such as finding the global past and future asymptotic solutions of these systems. At the hand of locally rotationally symmetric Bianchi types I, II and III, I will introduce the idea to view these systems as a periodic perturbation problem, and motivate the application of averaging methods.
The standard theory of averaging in nonlinear dynamical systems deals with problems where the perturbation is controlled by a constant parameter. In the presented case the perturbation is controlled by the Hubble scalar, a time dependent quantity. Since for the considered problems the Hubble scalar goes to zero as time goes to infinity, I will conjecture that the respective full and averaged solutions converge. This would allow one to find the future stable solution of the full system by finding that of the simpler averaged system, and I will present this for the above symmetry types. I will give numerical and analytical support to this conjecture, and sketch a potential proof.

Abstract: We discuss the relation between the canonical Hamilton-Jacobi theory and the De Donder-Weyl Hamilton-Jacobi theory known in the calculus of variations using the examples of a scalar field on curved space-time background and general relativity. By restricting ourselves to Gaussian coordinates, we show how the canonical Hamilton-Jacobi equation of general relativity can be derived from the De Donder-Weyl Hamilton-Jacobi reformulation of the Einstein equations.

Abstract: Spacetime curvature induces tidal forces on the wave function of a single quantum system. Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces. The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold. Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

Abstract: In this talk, we study a recent result on the development of the global-in-time existence, uniqueness and asymptotic stability for solutions nearby the relativistic Maxwellian to the special relativistic Boltzmann equation without any angular cutoff. In the physical situation, the angular function in the collision kernel is not locally integrable, and the collision operator behaves like a fractional diffusion operator. This resolves the open question of perturbative global existence without the Grad's angular cut-off assumption. This is a joint-work with Robert M. Strain.

Abstract: We investigate the stability of the Positive Mass Theorem for three-dimensional axisymmetric manifolds. It is widely known that asymptotically at manifolds with nonnegative scalar curvature have nonnegative ADM mass, and that the only asymptotically at manifold with nonnegative scalar curvature and zero ADM mass is Euclidean space. We will show that axisymmetric manifolds with nonnegative scalar curvature and small ADM mass, and which satisfy an additional technical assumption, are close to Euclidean space in a Sobolev sense.

Abstract: I will discuss recent results in modeling stationary self-gravitating tori (disks) around black holes. Special emphasis will be put on general-relativistic Keplerian rotation in self-gravitating perfect-fluid tori and the interaction between the angular momentum of the torus and the spin of the black hole. Next, I will focus on general-relativistic effects characteristic for sufficiently massive tori: bifurcations in the parameter space of solutions, the existence of toroidal ergoregions connected with the tori, the appearance of local maxima of the circumferential radius, and the properties of circular, equatorial geodesics in the obtained spacetimes.

Abstract: The Riemannian Penrose inequality is a fundamental result in mathematical general relativity and provides an estimate for the area of an outermost minimal surface in an asymptotically flat three-manifold solely in terms of the global mass. It was originally proven by Huisken and Illmanen using a weak version of the inverse mean curvature flow which has the crucial property of evolving the so-called Hawking mass in a non-decreasing way. In this talk, I will present a recent result which shows that a suitable version of the Penrose inequality continues to hold if the ambient manifold has a non-compact boundary. The main ingredient in the proof is a free boundary version of the weak inverse mean curvature flow which is obtained as the limit of a new approximation scheme accommodating for the presence of the non-compact boundary.

Abstract: In this talk I will introduce a new definition of spherically symmetric elastic body in Newtonian gravity. Using this new definition it is possible to introduce Milne-type homology invariant variables which transform the field equations into an autonomous system of nonlinear differential equations. By employing dynamical systems methods I will finally discuss the existence of static balls for a wide variety of constitutive equations, including Seth, Signorini, Saint Venant-Kirchhoff, Hadamard, and John’s harmonic materials.

Abstract: We discuss the different notions of charges for asymptotically de Sitter space-time. We present a covariant phase space construction of hamiltonian generators of asymptotic symmetries with `Dirichlet' boundary conditions in de Sitter spacetime, extending a previous study of J\"ager. We show that the de Sitter charges so defined are identical to those of Ashtekar, Bonga, and Kesavan (ABK). We then present a comparison of ABK charges with other notions of de Sitter charges. We compare ABK charges with counterterm charges, showing that they differ only by a constant offset, which is determined in terms of the boundary metric alone. We also compare ABK charges with charges defined by Kelly and Marolf at spatial infinity of de Sitter spacetime. When the formalisms can be compared, we show that the two definitions agree.

Abstract: In this talk I will discuss some features of the geometry of the Kerr metric near its singular ring. Based on joint work with Piotr Chrusciel and NicolaS Yunez.

Abstract: The vacuum Einstein equations, written in "harmonic" or "wave coordinates", are a system of nonlinear wave equations. Interestingly, very similar equations exhibit finite-time blowup, while the Einstein equations themselves admit global solutions for small initial data. The extra structure which enables them to avoid blowup is called the "weak null structure". In this talk I will explore this structure, giving a general definition and then some subclasses for which we can prove global existence for small initial data. I will also give some details of the proof of global existence for solutions to these classes of equations.

Abstract: I will propose a covariant definition of standing gravitational waves.

Abstract: Assuming U(1) symmetry of solutions we construct a fully constrained scheme for Einstein equations on compact spatial domains with S2 x S1 and S3 topology. Performing Geroch reduction and choosing appropriate gauge we rewrite Einstein equations into a system of elliptic and hyperbolic equations which are suitable for numerical computations. Following the approach of Beyer, Escobar and Frauendiener we use spin-weighted spherical harmonics to deal with the singularities of spherical polar coordinates. We apply the scheme to rotating cosmologies initial data with U(1)xU(1) symmetry found by Bizoń, Simon and Pletka.

Abstract: In joint work with Peter Hintz and András Vasy, we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild and slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. In this talk, I will describe the geometric background and the analytic setup of our result, including a discussion of gauge fixing. Our proof is based on a precise description of the resolvent of an associated wave equation on symmetric 2-tensors near zero energy.

Abstract: The action functional of the supersymmetric nonlinear sigma model is an important model in modern quantum field theory. From a mathematical point of view it consists of a map between two manifolds and a vector spinor defined along that map.
If one chooses a Riemannian domain manifold its critical points couple the elliptic harmonic map equation with the vector spinor, this system became known as Diracharmonic maps and variants thereof. Since the action functional of the supersymmetric nonlinear sigma model is unbounded from below it is very difficult to obtain existence results for this system.
However, in the case of a globally hyperbolic domain manifold the critical points lead to the Dirac‐wave map system which is a hyperbolic system of partial differential equations. In this setup unbounded action functionals are much better to deal with. We will present an existence result for wave maps and Dirac‐wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. This is joint work with Klaus Kröncke.

Abstract: When can you remove a singularity of spacetime by coor‐dinate transformation? I will report on our recent discovery of a system of nonlinear elliptic PDE's on spacetime, the Regularity Transformation equations (RT‐equations), which determine whether a non‐optimal connection Γ can be smoothed to optimal regularity by coordinate transformation, (i.e., to one derivative smoother than its Riemann curvature tensor Riem(Γ)). The RT‐equations apply to connections on a tangent bundle Tℳ of an arbitrary manifold ℳ, including semi‐Riemannian and Lorentzian manifolds of Relativity. By developing an existence theory for the nonlinear RT‐equations for such connections in L^∞, we prove that optimal connection regularity W^1;p (any p < ∞) can always be achieved and that no regularity singularities exist at GR shock waves. The celebrated curvature bounds of Uhlenbeck (a topic of this year's Abel prize) are deeply related to Riemannian geometry. We managed to extend these curvature bounds to connections on tangent bundles of Lorentzian manifolds, the setting of relativistic Physics, because the RT‐equations are elliptic regardless of metric signature.

Abstract: It is well known that photons, as particles, follow null geodesics in General Relativity. The corresponding wave dynamic is modelled by the Maxwell equations. The actual motion of the photon can be recovered, at least locally, by considering high-frequency solutions to the Maxwell equations. Nonetheless, it is well-known that the dynamics of wave packets can differ sensibly from the motion of the actual particles. One of this effect, known as the spin Hall effect, has been described for Maxwell equations propagating in a medium and observed mid-00. This can be explained by the spin degree of freedom of the particle interacting with the medium in which it propagates. In this collaboration, we propose to extend this notion of spin Hall effect to Maxwell field propagating on a curved background. The effective equation of motion describing the evolution of the wave packet can be compared with the equations of motions of spinning particles in General Relativity. We are in particular trying to develop a covariant approach to the construction of a WKB Ansatz for Maxwell field on curved backgrounds.
This is a collaboration with L. Andersson (AEI), M. Oancea (AEI), C. Paganini (Monash), I. Dodin (Princeton Plasma Physics Laboratory), and D. Ruiz (Sandia Laboratory).

Abstract: We consider the four-dimensional Einstein-$\Lambda$-Klein-Gordon system with mass $\mu^2=\frac{2}{3} \Lambda<0$. This system is known to posses a family of regular static solutions (solitons) satisfying Robin boundary conditions at infinity. We establish rigorously the existence of the solitons and some of their properties (in particular, the mass curve). We give numerical evidence for the nonlinear stability of solitons and construct time-periodic solutions inside and outside the homoclinic loops of the anti-de Sitter solution.

Abstract: I will discuss first order perturbations of guided electromagnetic waves which arise due to Earth's rotation (both around the sun and its own axis). Considering cylindrical waveguides as an example, the correction to the dispersion relation is computed and it is shown that nearby angular modes are coupled, giving rise to sidebands.

Abstract: After introductory remarks on the classical/quantum alternative I will discuss mainly the possibility of using gravity as an entanglement mediator as detailed in recent papers by Belenchia, Wald et al. and briefly the practical impossibility of single graviton detection.

Abstract: The distribution of the non-luminous matter in galaxies of different luminosity and Hubble type is much more than a proof of the existence of dark particles governing the structures of the Universe. The deeper we go into the knowledge of the dark component that embeds the stellar component of galaxies, the more we realize the profound interconnection present between the two of them.
They are too complex to be arisen by two inert components that just share the same Gravitational field.
The 30 years old paradigm which rests on a-priori knowledge of the nature of dark matter that has led to the scenario of collisionless dark matter in galaxy halos reveals itself to be insufficient to explain the observations. Here, we will review the complex but well-ordered scenario of the properties of the dark halos in relation with those of the baryonic components they host.
We will present a number of tight and unexpected correlations between selected properties of the dark and the luminous matter that indicate that they interacted in a direct way over the Hubble Time.

Abstract: While visiting Paul Romatschke at CU Boulder this spring, I started working on the resummation scheme, he introduced earlier this year (arXiv:1901.05483). I will give an overview of this scheme, following the original paper. This very versatile scheme (finite temperature, various dimensions, bosons/fermions) can be implemented numerically (only 1-loop integrals) and allows to determine transport coefficients. Further it is designed to perform calculations at finite coupling.
In this talk I want to show how we apply this scheme to the Gross-Neveu model in 1+1 dimensions.

Abstract: We find necessary and sufficient conditions ensuring that the vacuum development of an initial data set of the Einstein's field equations admits a conformal Killing vector. We refer to these conditions as conformal Killing initial data (CKID) and they extend the well-known Killing initial data that have been known for a long time. The strategy used to find the CKID is a classical argument involving wave-like "propagation equations". Time permitting, I will how similar strategies might succeed or fail for other geometric equations, like e.g. Killing-Yano.

Abstract: We consider the wave equation, $\square_g\psi=0$, in fixed flat Friedmann-Lemaître-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface $\{t=0\}$. The initial data sets are characterized by the condition that the Neumann data should dominate, in an appropriate $L^2$-sense, up to two spatial derivatives of the Dirichlet data. For these initial configurations, the $L^2(\mathbb{T}^3)$ norms of the solutions blow up towards the Big Bang hypersurfaces of FLRW and Kasner with inverse polynomial and logarithmic rates respectively. Our method is based on deriving suitably weighted energy estimates in physical space. No symmetries of solutions are assumed.

Abstract: We derive generic properties of non-extremal horizons, assumed to be in equilibrium with a thermal bath, in any spacetime dimension greater than two. The physical properties of the thermal bath are modelled by the way we impose boundary conditions, and we shall describe various different well-motivated choices leading to infinite-dimensional near horizon symmetries, including BMS-like symmetries for arbitrary spin and Heisenberg-like symmetries. We prove that they generically span soft hair excitations in the sense of Hawking, Perry and Strominger.

Abstract: Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. We focus on non-expanding waves which later have been generalised to impulses travelling in all constant-curvature backgrounds. While Penrose's original construction was based on his vivid geometric 'scissors-and-paste' approach in a flat background, until now a comparably powerful visualisation and understanding have been missing in the ${? not=0}$ case. In this work we provide such a picture: The (anti-)de Sitter hyperboloid is cut along the null wave surface, and the 'halves' are then re-attached with a specific shift of their null generators across the wave surface.

Abstract: Free higher-spin Fronsdal fields generalise Maxwell fields and linearised gravity to higher tensor fields. Whereas for spin-1 and spin-2 there are non-linear completions (e.g. Yang-Mills, gravity), no non-linear, gauge-invariant theory of Fronsdal fields is known. A systematic way to construct them is the Noether procedure in which a gauge invariant action is constructed in a perturbative expansion in powers of the fields. In three space-time dimensions, there are strong obstructions to construct such an action leading to the conclusion that the interactions of the higher-spin gauge fields are completely fixed by the cubic vertices in the action.

Abstract: The Vlasov-Maxwell system is a classical model in plasma physics. Glassey and Strauss proved global existence for the small data solutions of this system under a compact support assumption on the initial data. I will present how vector field methods can be applied to revisit this problem. In particular, it allows to remove all compact support assumptions on the initial data and obtain sharp asymptotics on the solutions. We will also discuss the null structure of the system which constitutes a crucial element of the proof.

Abstract: The black hole stability problem, i.e. problem of proving dynamical stability of the Kerr family of rotating black hole spacetimes, is one of the major open problems in general relativity. Linearized stability is an important step toward solving the black hole stability problem. In this talk, based on the recent paper https://arxiv.org/abs/1903.03859, joint with Bäckdahl, Blue, and Ma, I will describe our proof of linearized stability, and explain the role of the special geometry of the Kerr spacetime in the stability problem

Abstract: The equations of motion of massless test particles with spin are discussed and solved in the Schwarzschild metric.

Abstract: The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach set-up in the non-relativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The origin of this difficulty lies in the fact that, on the one hand, the spin gets entangled with the momentum in Lorentz-boosted reference frames, and on the other hand, for a particle moving in a superposition of velocities, it is impossible to "jump" to its rest frame, where spin is unambigously defined. In this talk, I will introduce a quantum reference frame transformation corresponding to a "superposition of Lorentz boosts," allowing us to transform to the rest frame of a particle that is in a superposition of relativistic momenta with respect to the laboratory frame. This enables us to first move to the particle's rest frame, define there the spin measurements (via the Stern-Gerlach experimental procedure), and then move back to the laboratory frame. In this way, we find a set of "relativistic Stern-Gerlach measurements" in the laboratory frame, and a set of observables satisfying the spin su(2) algebra. This operational procedure offers a concrete way of testing the relativistic features of the spin, and opens to the possibility of devising quantum information protocols for spin in the special-relativistic regime.

Abstract: In general relativity light propagation is affected by gravity, leading to the well-known effects of light bending, Shapiro delays and gravitational redshift. On top of that the results of observation of light by an observer are also affected by the special relativistic phenomena like the aberration or time dilation. All these effects influence the measurements of shape, parallax, redshift and position drift (proper motion) of distant objects. We show that all results of those measurements can be understood as functions of the curvature along the line of sight. This opens up the possibility to probe the spacetime curvature directly using only optical observations.

Abstract: In the first part of this talk, we present an elementary proof of the rigidity of the hyperbolic space as the unique Poincaré-Einstein manifold whose boundary at infinity is the conformal round sphere. The proof relies on an inequality which relates the Yamabe invariant of the boundary with the one of a compactification of the bulk manifold. In a second part, we relate the Cheeger constant of such manifolds with the conformal type of the boundary at infinity . More precisely, we prove that this constant is exactly the dimension of the interior of the Poincaré-Einstein manifold if and only if the Yamabe invariant of the boundary is non negative. Several applications are then discussed.

Abstract: The asymptotic symmetries of gravity and electromagnetism are remarkably rich. The talk will explain the asymptotic structure of gravity and electromagnetism in the asymptotically flat case by making central use of the Hamiltonian formalism. In particular, how the relevant infinite-dimensional asymptotic symmetry groups emerge at spatial infinity, and the extension to higher spacetime dimensions, will be discussed.

Abstract: We analyse the Kantowski-Sachs cosmologies with Vlasov matter of massive and massless particles using dynamical systems analysis. We show that generic solutions are past and future asymptotic to the non-flat locally rotationally symmetric Kasner vacuum solution. Furthermore, we establish that solutions with massive Vlasov matter behave like solutions with massless Vlasov matter towards the singularities.

Abstract: A convenient approach to analyze spatial infinity is to use a cylinder representation and impose a gauge based on a congruence of conformal geodesics. This so-called conformal Gauss gauge comes along with the freedom to specify initial data for the conformal geodesics. Such a gauge has been constructed from an ordinary Cauchy surface and from past null infinity, respectively. In this talk we compare these gauges near the critical set, where the cylinder "touches" past null infinity, as it turns out that they are related in a somewhat unexpected intricate way.

Abstract: I will discuss dynamics of small amplitude solutions of the Schroedinger-Newton system with an external harmonic potential. This system arises in a nonrelativistic limit from the Einstein-Klein-Gordon equations with a negative cosmological constant. The main goal is to understand the resonant transfer of energy to small spatial scales.

Abstract: I will present the proof of positivity of hyperbolic mass in all dimensions for asymptotically hyperbolic manifolds with spherical conformal infinity. Based on joint work with Erwann Delay arXiv:1901.05263

Abstract: The Milne cosmological model, a specific case of the FLRW family of cosmologies, represents an expanding universe emanating from a big bang singularity with a linear scale factor. With such a slow expansion rate, particularly compared to related isotropically expanding models (such as de Sitter), there are interesting questions one can ask about stability of this spacetime. For example previous results have shown that, when looking at the initial value problem, the Milne model is a stable solution to the vacuum Einstein, Einstein-Klein-Gordon and Einstein-Vlasov systems. Motivated by the last result, I will discuss our proof of the stability of the Milne model to the Einstein-Klein-Gordon system. This was shown recently by J. Wang using an alternative gauge and method. Thus I will also give comparisons between our method and results. This is joint work with D. Fajman.

Abstract: We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open, and may differ from the corresponding sets defined via piecewise C1-curves. By refining the notion of a causal bubble from [P. T. Chruściel and J. D. E. Grant. On Lorentzian causality with continuous metrics. Classical Quantum Gravity 2012], we characterize spacetimes for which such phenomena can occur, and also relate these to the possibility of deforming causal curves of positive length into timelike curves (push-up). The phenomena described here are, in particular, relevant for recent synthetic approaches to low regularity Lorentzian geometry where, in the absence of a differentiable structure, causality has to be based on locally Lipschitz curves.

Abstract: In 2009 Dafermos and Rodnianski introduced a new approach to decay estimates of wave equations on a Lorentzian background. Instead of using global vector field multipliers and commutators with weights in t, they developed a heirarchy of estimates coming from r^p weighted vector fields. In this talk I will introduce their method applied to Minkowski and Schwarzschild spacetimes and outline some of the reasons why their method is particularly useful when dealing with Schwarzschild and Kerr background metrics. SC005336.

Abstract: I will present some recent results concerning the Strong Cosmic Censorship Conjecture (SCCC) in the presence of a positive cosmological constant. I will start by reviewing some of the progress made in the context of the Einstein-Maxwell-scalar field system in spherical symmetry and the linear wave equation in the black hole interior of Reissner-Nordström de Sitter. These results show that the validity of the SCCC hinges on the precise decay rates of perturbations along the event horizon which are known to be determined by the black hole's quasinormal spectrum. I will also discuss recent numerical computations of quasinormal modes that suggest the failure of th SCCC in a near extremal regime of charged de Sitter black holes.

Abstract: Recently, a lot of work has been done on characterisation of black hole horizons in the near horizon limit. It has been shown that three dimensional black holes admit near horizon Heisenberg algebras. This allows these black holes to be dressed with soft hair. The term soft refers to the description of a symmetry generator whose action on a state does not modify the energy of that state. This implies that black holes are characterised by their three fundamental parameters (mass, angular momentum, and electric charge) and also by their soft hair content. The development of the theory of soft hair has in turn led to numerous developments.
In this talk, I will initially consider the near horizon physics of black holes in an arbitrary number dimensions, eventually focusing on the four dimensional case. I will present consistent sets of boundary conditions defined at the black hole horizon and discuss their symmetry algebras. One of them is made of the Heisenberg algebras and have soft hair in the charge spectrum. This opens up new directions to discuss several issues of the black hole physics.

Abstract: I will discuss (I) the De Donder-Weyl (DW) Hamiltonian and Hamilton-Jacobi formulation of classical fields and the underlying mathematical structures which can be used for quantization (the polysymplectic structure and the Poisson-Gerstenhaber brackets), (II) a field quantization based on those structures (precanonical quantization) which leads to a hypercomplex rather than infinite-dimensional generalization of quantum theory as a description of quantum fields, (III) examples of precanonical quantization of a nonlinear scalar field on flat and curved background, and the pure Yang-Mills field, (IV) the consistency of precanonical quantization with the Ehrenfest theorem, (V) the relation to the standard QFT in the functional Schrödinger representation, which appears as a singular limiting case, (VI) precanonical quantization of general relativity in vielbein Palatini formulation and the spin-connection foam picture of quantum geometry of space-time it leads to.

Abstract: Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference systems. In this talk, I will summarize a recent systematic method for such switches, which works in analogy to coordinate changes on a manifold, except that these `quantum coordinate changes' proceed between different Hilbert spaces.
I will illustrate this method by means of spatial quantum reference frames and a simple quantum cosmological model. Time permitting, I might also disucss conceptual implications for quantum gravity. (Based on arXiv:1809.00556, 1809.05093, 1810.04153 and 1811.00611.)

Abstract: The Ricci curvature is the basic ingredient in the Einstein equations of general relativity. In recent years the interpretation of Ricci curvature in Riemannian geometry has changed fundamentally via its characterization in terms of convexity properties of e.g. the Shannon-Bolzmann entropy of optimal transportation. In my talk I will explain the recent development of an analogous characterization of Ricci curvature in Lorentzian geometry.

Abstract: Static vacuum metrics are solutions to the Einstein Field Equations with vanishing stress-energy tensor and featuring a very special metric structure (warped product). Such a structure induces a natural foliation of the spacetime into space-like slices which are all isometric to each other, so that the corresponding physical universe is static.
We discuss the problem of the classification of such solutions in the case of positive cosmological constant. To this end, we introduce an appropriate notion of mass, showing that it satisfies a Positive Mass Statement and a Riemannian Penrose-like inequality. Building on this, we prove a uniqueness result for the Schwarzschild-de Sitter solution, which is somehow reminiscent of the well known Black Hole Uniqueness Theorem for the Schwarzschild solution.

Abstract: The structure of spherically symmetric static solutions is quite well understood and I will discuss a number of their features since they indicate what features can be expected of axisymmetric solutions. Existence of axially symmetric stationary solutions that are perturbed off from spherically symmetric Newtonian solutions have been obtained analytically whereas solutions far from spherically symmetric have only been constructed numerically. I will discuss the properties of the latter. In particular, two different sequences of toroidal solutions which contain ergoregions will be described in detail. These solutions either approach an extreme Kerr black hole or they have the property that the geometry becomes conical in the limit and such solutions may provide models of cosmic strings.

Abstract: In the last 30 years an enormous amount of work has been done on the existence and global structure of asymptotically flat solutions to Einstein's field equations. Many of these contributions are in themselves fairly complete. There are, however, still gaps in the general understanding. In this talk I shall discuss some questions whose answers would result in a more complete overall picture of the situation.

Abstract: In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g₀ consists of a set of tensorial equations T [g] = 0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is locally isometric to the reference spacetime metric g₀. We give the first IDEAL characterization of generalized Schwarzschild-Tangherlini spacetimes, which consist of Λ-vacuum extensions of higher dimensional spherically symmetric black holes, as well as their versions where spheres are replaced by flat or hyperbolic spaces. The standard Schwarzschild black hole has been previously characterized in the work of Ferrando and Sáez, but using methods highly specific to 4 dimensions. Specialized to 4 dimensions, our result provides an independent, alternative characterization. We also give a proof of a version of Birkhoff’s theorem that is applicable also on neighborhoods of horizon and horizon bifurca-tion points, which is necessary for our arguments.

Abstract: The Killing operator $K_{ab}[v]=\nabla_a v_b + \nabla_b v_a$ is the generator of gauge symmetries (linearized diffeomorphisms) $h_{ab}\mapsto h_{ab} + K_{ab}[v]$ in linearized gravity. A linear local gauge-invariant observable is a differential operator $I[h]$ such that $I[K[v]] = 0$ for any gauge parameter field $v_a$. A set $\{I_i[h]\}$ of such observables is complete if the simultaneous conditions $I_i[h] = 0$ are sufficient to conclude that the argument is a pure gauge mode, $h_{ab} = K_{ab}[v]$. The explicit knowledge of a complete set of local gauge invariant observables has multiple applications from the points of view of both physics and geometry, whenever a precise separation of physical and gauge degrees of freedom is required. Surprisingly, until very recently, such complete sets have been known explicitly only on spacetimes of maximal symmetry (Minkowski or (anti-)de Sitter). I will discuss recent progress that has allowed an explicit construction of complete sets of local gauge invariant observables on backgrounds of sub-maximal symmetry, most notably on cosmological (FLRW) and black hole (Schwarzschild and Kerr) spacetimes.

Abstract: The construction of initial data for the Cauchy problem in General Relativity is an interesting problem from both the mathematical and physical points of view. As such, there have been numerous methods studied in the literature - the "Conformal Method" of Lichnerowicz-Choquet-Bruhat-York and the "gluing" method of Corvino-Schoen being perhaps the best-explored.
In this talk I will describe an alternative, perturbative, approach proposed by A. Butscher and H. Friedrich, and show how it can be used to construct non-linear perturbations of initial data for spatially-closed analogues of the "k = -1" FLRW spacetime. Time permitting, I will discuss possible refinements/extensions of the method, along with its generalisation to the full Conformal Constraint Equations of H. Friedrich.

Abstract: Conformal gravity is a higher derivative gravitational theory that is conformally invariant, in addition to its diffeomorphism invariance. In four dimensions the conformal gravity Lagrangian contains up to four derivatives of the metric. Like most higher derivative theories, a naive analysis yields that conformal gravity is power-counting renormalizable at the prize of introducing ghost degrees of freedom, in contrast to general relativity, which is power-counting non-renormalizable but has no ghosts. The theory has been considered in several contexts in the literature, such as a quantum gravity, cosmology and holography.
Throughout our work, conformal gravity is examined in holographic, classical and semi-classical contents. At first, in order to establish the structure of a possible holographic dual the theory is considered in the holographic approach. In particular, conformal gravity is formulated with new, generalized asymptotic boundary conditions which allow for a term compatible with the most general spherically symmetric solution of the theory, namely an asymptotically subleading Rindler term. The conformal gravity action with the proposed asymptotic boundary conditions is proven to constitute a well-defined variational principle and the corresponding response functions are shown to be nite. Therefore, no additional boundary terms or holographic counterterms are required to be added at the level of the action. The obtained results for the response functions are applied to phenomenologically interesting examples. Furthermore, the asymptotic symmetry algebras of the dual field theory are constructed and they are classified according to their number of generators. It turns out that the highest-dimensional subalgebra consists of 5 generators. Then, classical aspects of conformal gravity are examined via the Hamiltonian formulation of the theory. Namely, exploiting the constraint analysis, the generator of gauge symmetries is derived and then, using slightly more generalized boundary conditions compared to the ones of the holographic analysis, the canonical charges associated with asymptotic symmetries are constructed. No charges associated with local Weyl rescalings are found. Thus, the obtained charges are associated with asymptotic spacetime diffeomorphisms and their asymptotic symmetry algebra is the algebra of boundary conditions preserving diffeomorphisms. Finally, conformal gravity is considered in the semi-classical approximation. This is done by analytically evaluating the 1-loop partition function of the theory, using heat kernel techniques.

Abstract: In this talk I’m going to present our recent studies on gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of non-spherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.

Abstract: We construct Einstein metrics of negative sectional curvature on ramified covers of compact hyperbolic four-manifolds with symmetries, initially considered by Gromov and Thurston. These metrics are obtained through a deformation procedure. The approximate Einstein metric is an interpolation between a black-hole Einstein metric near the branch locus and the pulled-back hyperbolic metric. The deformation relies on an involved bootstrap procedure. Our construction yields the first example of compact Einstein manifolds with negative sectional curvature which are not locally homogeneous. This is a joint work with J. Fine (ULB).

Abstract: 3-dimensional null surfaces that are Killing horizons to the second order are considered. They are embedded in 4-dimensional spacetimes that satisfy the vacuum Einstein equations with arbitrary cosmological constant. Internal geometry of 2-dimensional cross sections of the horizons consists of induced metric tensor and a rotation 1-form potential. It is subject to the type D equation.
The equation is interesting from the both, mathematical and physical points of view. Mathematically it involves geometry, holomorphic structures and algebraic topology. Physically, the equation knows the secrete of black holes: the only axisymmetric solutions on topological sphere correspond to the the Kerr / Kerr-de Sitter / Kerr-anti-de-Sitter non-extremal black holes or to the near horizon limit of the extremal ones. In the case of bifurcated horizons the type D equation implies another spacial symmetry. In this way the axial symmetry may be ensured without the rigidity theorem. The type D equation does not allow rotating horizons of topology different then that of the sphere (or its quotient). That completes a new local no-herr theorem. The type D equation is also an integrability condition for the Near Horizon Geometry equation and leads to new results on the solution existence issue.

Abstract: I will describe recent results with K. Prabhu that show positivity of the canonical energy of perturbations of Schwarzschild that are obtained from a Hertz potential. We will also show how the energy quantity arising in the Schwarzschild stability proof of Dafermos, Holzegel, and Rodnianski is related to Hertz potentials and canonical energy. Much of the talk will be spent reviewing canonical energy and Hertz potentials.

Abstract: Taking nonrelativistic limits of field systems in Anti-de Sitter (AdS) spacetime results in variants of the Gross-Pitaevskii equation describing cold atomic gases in harmonic traps (which can be implemented in contemporary terrestrial experiments). This relation underlies the similarities in weakly nonlinear dynamics of these two classes of systems (AdS and atomic gases) whose investigation is normally motivated by rather different physical goals (phenomenology of Bose-Einstein condensation vs. studies of strongly coupled conformal field theories in the context of AdS holography). I will explain how the weakly nonlinear dynamics of such systems is analyzed via the so-called resonant approximation, and present a range of surprising exact results and open questions for the effective nonlinear resonant systems arising from such analysis.

Abstract: Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schrödinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter spacetime. The classical dynamics within this class of systems can be very rich, ranging from fully integrable to chaotic as one changes the values of the mode coupling coefficients. I'll report on investigations of quantum infinite-dimensional resonant systems, which are mathematically a highly special case of two-body interaction Hamiltonians (extensively studied in condensed matter, nuclear and high-energy physics).
Despite the complexity of the corresponding classical dynamics, the quantum version turns out to be remarkably simple, with the Hamiltonian being block-diagonal in the Fock basis, with all blocks of varying finite sizes. Being solvable in terms of diagonalizing finite numerical matrices, these systems are thus arguably the simplest quantum field theories known to man. I'll discuss how to perform the diagonalization in practice, and mention both numerical patterns emerging for the integrable cases, and the spectral statistics, which efficiently distinguishes the special integrable cases from generic (chaotic) points in the parameter space. A wide range of further potential applications can be envisaged, due to the computational simplicity and dynamical richness of quantum resonant systems.

Abstract: In this informal talk, we will make a short case against the inflationary paradigm by highlighting some of its problems. In doing so, it will be clear that other alternatives scenarios should also be considered, as for example bouncing cosmologies and emergent quantum gravity proposals. Then we will focus on the latter, in particular in the context of string theory, which prevails being the unique quantum gravity theory that is viable for an unification with the other interactions. We finally discuss String Gas Model and recent developments in the field.

Abstract: For Laplace operator in various regions the problem of existence and properties of eigenvalues and eigenfuctions have been extensively studied and an almost complete theory emerged. In contrast similar theory for the linearised hydrodynamics with different boundary conditions is not existent as the relevant operator is not normal and general tools of the theory of self adjoint operators cannot be applied. I will describe a method to prove existence and completness of the spectrum of linearised hydrodynamics and basic properties of the eigenfunctions.

Abstract: Motivated by the conformal method of solving the constraints in General Relativity, R. Beig and W. Krammer defined, on any 3-dimensional conformally flat Riemannian manifold M, a symmetric, tracefree two-tensor as the tensor product of an arbitrary vector V and a conformal Killing vector W.
If V is divergence free, so is the Beig-Krammer tensor - hence it can serve as ADM momentum density in vacuum, (possibly with cosmological constant).
We examine the very special case that M is the round three sphere and that V and W are Killing vectors, and compare with the known "donut" case.
The application of this tensor to the initial value problem becomes particulary interesting in view of a recent theorem by Premoselli which in essence settles the question of (non-)existence of solutions of the Lichnerowicz equation on compact Riemannian three manifolds.
This is joint and ongoing work with Piotr Bizon.

Abstract: In this talk, I will discuss a new approach to establishing the well-posedness of the relativistic Euler equations for liquid bodies in vacuum. The approach is based on a wave formulation of the relativistic Euler equations that consists of a system of non-linear wave equations in divergence form together with a combination of acoustic and Dirichlet boundary conditions. The equations and boundary conditions of the wave formulation differs from the standard one by terms proportional to certain constraints, and one of the main technical problems to overcome is to show that these constraints propagate, which is necessary to ensure that solutions of the wave formulation determine solutions to the Euler equations with vacuum boundary conditions. During the talk, I will describe the derivation of the wave equation and boundary conditions, the origin of the constraints, and how one shows that the constraints propagate. Time permitting, I will also discuss how energy estimates can be obtained from this new formulation paying particular attention to the role of the acoustic boundary conditions.

Abstract: I will discuss the problem of proving the stability of the family of Kerr-de Sitter (KdS) black holes as solutions of Einstein's vacuum equation: spacetimes evolving from initial data close to those of $(M,g)$ stay globally close to $(M,g)$, and are indeed asymptotic to $(M,g)$ or another nearby member of the KdS family.
I will focus on analytic aspects of this problem together with the choice of a gauge to break the diffeomorphism invariance of Einstein's equation and the role of constraint damping. The analytic framework is that of global non-elliptic Fredholm problems. The main ingredients are, first, the microlocal control of the regularity of waves by means of elliptic, real principal type, and radial point estimates on a suitable compactification of the spacetime; and second, the asymptotic analysis in which model operators and resonance expansions play a role.

Abstract: In recent years, quantum correlations have gained a prominent role in many areas of physics, from quantum information science to tests of alternative theories of gravity. Quantum correlations are the core ingredient of many tasks in the most diverse areas of science, such as quantum refrigeration, quantum communication or the Hawking effect. A thorough investigation of the nature of these correlations and their role is paramount to advance our knowledge of nature.
We present a body of work that aims at understanding the role of quantum correlations in phenomena that exhibit genuine relativistic and quantum features. This body of work covers different aspects of relativistic quantum physics, from quantum communication in curved spacetimes, to ultra-precise measurements of the gravitational field and the contributions of quantum correlations in the theory of gravitation. We discuss possible applications and potential attempts for experimental demonstrations.

Abstract: Bartnik data are a Riemannian 2-sphere of positive Gaussian curvature equipped with a non-negative function H to be thought of as its mean curvature in an ambient Riemannian 3-manifold. Mantoulidis and Schoen suggested a construction of asymptotically flat Riemannian 3-manifolds of non-negative scalar curvature which allows to isometrically embed given Bartnik data of vanishing mean curvature, i.e. H=0. They use their construction to explore — and disprove — stability of the Riemannian Penrose inequality. In collaboration with Cabrera Pacheco, McCormick, and Miao, we adapt their construction to constant mean curvature (CMC) Bartnik data, i.e. H=const.>0. Moreover, with Cabrera Pacheco and McCormick, we extend their construction to the asymptotically hyperbolic setting both for H=0 and for H=const.>0 Bartnik data.
I will present the construction as well as the motivation for such a construction which is related to Bartnik’s quasi-local capacity/mass functional and its minimizing properties.

Abstract: Cosmological observations have established that our universe has positive cosmological constant. A positive cosmological constant profoundly alters the asymptotic structure of space-time. In this talk, we discuss the linearized gravitational field produced by compact sources in the background with positive cosmological constant -- de Sitter space. Using the covariant phase space formalism, we obtain the quadrupole formula in such a setting. We also show that the energy flux of gravitational waves measured at future null infinity is the same as that measured across the cosmological horizon of the compact source. To get an order of estimate we also discuss power radiated by a binary system in de Sitter background.

Abstract: I am going to present the research I have done for my Master’s and my PhD theses.
For the former, at the University of Vienna, I worked with Mark Heinzle on spatially homogenous cosmology and dynamical systems. We determined the past and future asymptotic dynamics of a particular class of models, locally rotationally symmetric Bianchi type VIII with an anisotropic fluid, and investigated the question if anisotropic matter matters. It does!
For the latter, at Cardiff University and in the LIGO Scientific Collaboration, I worked with Mark Hannam on initial data for black hole simulations. I will explain what trumpet initial data is and why it is of interest, in particular with regards to binary black hole simulations for gravitational wave extraction, and how this ties in with the LSC’s task of detecting gravitational waves in the broader context. I will present our numerical approach to derive trumpet initial data for Schwarzschild and extreme Kerr black holes, and argue that it should be generalisable to slow Kerr as well.

Abstract: The well-known theorem of Choquet-Bruhat and Geroch states that for given smooth initial data for the Einstein equations there exists a unique maximal globally hyperbolic development. In particular, the time-evolution of globally hyperbolic solutions is unique. This talk investigates whether the same results hold for quasilinear wave equations defined on a fixed background. We first present an example of a quasilinear wave equation for which unique evolution of smooth globally hyperbolic solutions in fact fails and contrast this case with the Einstein equations. We then proceed by presenting conditions which guarantee unique evolution. This talk is based on joint work with Felicity Eperon and Harvey Reall

Abstract: In this talk, the geometric framework of local metric deformations will be discussed with special emphasis on so-called generalized Kerr-Schild deformations. The consideration of precisely these deformations is justified by the fact that they lead to a comparably simple structure of Einstein's field equations, which is demonstrated using the spin-coefficient formalism of Newman and Penrose. Based on the results obtained, it is shown how the field of a gravitational shockwave generated by a massless point-like particle can be calculated at the event horizon of the stationary Kerr-Newman black hole, while specific physical properties of the corresponding class of geometries are discussed in passing.

Abstract: The Teukolsky master equation (TME) governs the dynamics of massless spin-$s$ fields in Kerr spacetime, $s=0,1,2$ corresponding to scalar field, electromagnetic field and linearized gravity respectively. In this talk, I will review the main progress on obtaining energy estimates and integrated local energy decay (Morawetz) estimates for these fields in Schwarzschild and Kerr spacetimes in the last decade, and then present the main ideas in my recent results on obtaining energy, Morawetz and pointwise decay estimates for TME in the cases of both Maxwell field and linearized gravity on Kerr backgrounds. Part of the work is joint work with Lars Andersson, Thomas Backdahl, Pieter Blue and Jinhua Wang.

Abstract: The ADM equations, properly understood, describe the change of first and second fundamental form of a spacelike slice under change of immersion of this slice. This viewpoint gives rise to a derivation of the ADM equations, which, contrary to existing derivations we are aware of, remains meaningful when the lapse is allowed to have zeros

Abstract: The Vlasov-Maxwell system is a classical model in plasma physics. Glassey-Strauss proved global existence for the small data solutions of this system under a compact support assumption on the initial data. They also established optimal decay rates for these solutions but not on their derivatives.We present here how vector field methods, developped by Christodoulou-Klainerman ([CK]) for the Maxwell equations (in 3d) and, more recently, by Fajman-Joudioux-Smulevici ([FJS]) for the Vlasov equation, can be applied to revisit this problem. In order to adapt the results of [CK] in high dimensions, and then obtain the optimal pointwise decay estimates on the null components of the electromagnetic field, we study the Vlasov-Maxwell system in the Lorenz gauge. We extend the techniques of [FJS] as we do not use a hyperboloidal foliation (and we then do not need any compact support assumption in space on the initial data) thanks to a new decay estimate for the velocity average of the Vlasov field. It allows us, by making crucial use of the null properties of the system, to remove all compact support assumptions on the initial data and to obtain optimal decay rates for the derivatives of the solutions. The work on the 3d case is in progress.

Abstract: Calabi-Yau spaces play an important role in compactifications of string theory from ten to four dimensions. In this talk I will show how Calabi-Yaus can be constructed and analyzed by making use of a supersymmetric gauge theory in two dimensions - the gauged linear sigma model. After introducing the basic concepts and examples, I will give an overview of recent applications.

Abstract: In this talk we consider Killing horizons which are such for two or more linearly independent Killing vectors. We provide a rigorous definition of these multiple Killing horizons (MKHs) an derive a couple of properties. We also present explicit examples of all possible types of MKHs. This is joint work with M. Mars and J. Senovilla.

Abstract: We discuss time quasi-periodic solutions to nonlinear Klein-Gordon equations on the torus in arbitrary dimensions. We will explain the result and the method, which is based on Anderson localization and algebraic geometry. 

Abstract:On the way towards a feasibility study of waveguide-based gravitational wave detection, the seminar will review the very basic calculations of interferometric gravitational wave detection within 3 different descriptions:
- lightlike geodesics (TT gauge)
- relativistic Maxwell equations (TT gauge)
- laboratory frame considerations (LL gauge)

Abstract: In string theory, our most developed theory of quantum gravity to date, one is interested in spacetimes of the form R^{1+3}_* K where K is some n-dimensional compact Ricci-flat manifold. In the first and simplest case considered by Kaluza and later Klein, K is the n-torus with the flat metric. An interesting question to ask is whether this solution to the Einstein equations, viewed as an initial value problem, is stable to small perturbations of the initial data. Motivated by this problem, I will outline the proof of stability in a restricted class of perturbations, and discuss the physical justification behind this restriction. Furthermore the resulting PDE system exhibits the weak-null condition, and I will discuss how it can be treated by generalising the proof of the non-linear stability of Minkowski spacetime given by Lindblad and Rodnianski.

Abstract: For metrics that are at least C^1,1 maximizing curves must be solutions of the geodesic equation and hence cannot change causal character: they must remain either timelike or null. This is no longer obvious for metrics of lower regularity and once the regularity drops below Lipschitz there are examples of "bubbling" metrics, for which maximizing causal curves may contain both timelike and null segments. We will present a recent result stating that Lipschitz regularity of the metric is sufficient for maximizing curves to have fixed causal character and show how this almost immediately gives a Lipschitz inextendibility result for timelike geodesically complete spacteimes. This is joint work with E. Ling.

Abstract: We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The role of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way we recover many fundamental results in greater generality, while at the same time clarifying the minimal requirements for and the interdependence of the basic building blocks of the theory. A main focus of this work is the introduction of synthetic curvature bounds, akin to the theory of Alexandrov and CAT(k)-spaces, based on triangle comparison. Applications include Lorentzian manifolds with metrics of low regularity, closed cone structures, and certain approaches to quantum gravity. This is joint work with Michael Kunzinger. Preprint: https://arxiv.org/abs/1711.08990

Abstract: After an introduction on gravitational waves and nonlinear effects in general, the talk will present the foundations of a new solution technique for the characteristic initial value problem of colliding plane gravitational waves. Assuming plane symmetry, the Einstein equations essentially reduce to the Ernst equation. In the course of the inverse scattering method this nonlinear PDE is tranlated first into an overdetermined linear system of differential equations and secondly into a Riemann-Hilbert problem. Ambiguities in this Riemann-Hilbert problem's solution lead to the construction of families of exact spacetimes generalising the proper solution to the initial value problem. Therefore the presented technique also serves as a solution generating technique. The method is exemplified by generalising the Szekeres class of colliding plane wave spacetimes. A new type of circularly polarised impulsive gravitational waves is identified within this generlisation.

Abstract: In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? The relational approach to physics suggests that all the features of a system —such as entanglement and superposition— are observer-dependent: what appears classical from our usual laboratory description might appear to be in a superposition, or entangled, from the point of view of such a quantum reference frame. In this work, we develop an operational framework for quantum theory to be applied within quantum reference frames. We find that, when reference frames are treated as quantum degrees of freedom, a more general transformation between reference frames has to be introduced. With this transformation we describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, which we explore in the case of ‘superposition of Galilean translations’ and ‘superposition of Galilean boosts’. In addition, we consider the situation when the reference frame moves in a ‘superposition of accelerations’, which leads us to extend the validity of the weak equivalence principle to quantum reference frames. Finally, this approach to quantum reference frames also has natural applications in defining the notion of the rest frame of a quantum system when it is in a superposition of momenta with respect to the laboratory frame of reference.

Abstract: We consider the limit a→∞ of the Kerr-de Sitter spacetime and analyze its global structure, with particular attention to its Killing horizons. This solution to Einstein's field equations with positive cosmological constant contains, apart from Λ, a unique free parameter which can be related to the angular momentum of one of its Killing horizons. A maximal extension of the (axis of the) spacetime is explicitly built. This is joint work with Marc Mars and Jose Senovilla.

Abstract: In this talk, the geometric framework of local metric deformations will be discussed with special emphasis on so-called generalized Kerr-Schild deformations. The consideration of precisely these deformations is justified by the fact that they lead to a comparably simple structure of Einstein's field equations, which is demonstrated using the spin-coefficient formalism of Newman and Penrose. Based on the results obtained, it is shown how the field of a gravitational shockwave generated by a massless point-like particle can be calculated at the event horizon of the stationary Kerr-Newman black hole, while specific physical properties of the corresponding class of geometries are discussed in passing.

Abstract: The Vlasov-Maxwell system is a classical model in plasma physics. Glassey-Strauss proved global existence for the small data solutions of this system under a compact support assumption on the initial data. They also established optimal decay rates for these solutions but not on their derivatives.
We present here how vector field methods, developped by Christodoulou-Klainerman ([CK]) for the Maxwell equations (in 3d) and, more recently, by Fajman-Joudioux-Smulevici ([FJS]) for the Vlasov equation, can be applied to revisit this problem. In order to adapt the results of [CK] in high dimensions, and then obtain the optimal pointwise decay estimates on the null components of the electromagnetic field, we study the Vlasov-Maxwell system in the Lorenz gauge. We extend the techniques of [FJS] as we do not use a hyperboloidal foliation (and we then do not need any compact support assumption in space on the initial data) thanks to a new decay estimate for the velocity average of the Vlasov field. It allows us, by making crucial use of the null properties of the system, to remove all compact support assumptions on the initial data and to obtain optimal decay rates for the derivatives of the solutions. The work on the 3d case is in progress.

Abstract: Calabi-Yau spaces play an important role in compactifications of string theory from ten to four dimensions. In this talk I will show how Calabi-Yaus can be constructed and analyzed by making use of a supersymmetric gauge theory in two dimensions - the gauged linear sigma model. After introducing the basic concepts and examples, I will give an overview of recent applications.

Abstract: In this talk we consider Killing horizons which are such for two or more linearly independent Killing vectors. We provide a rigorous definition of these multiple Killing horizons (MKHs) an derive a couple of properties. We also present explicit examples of all possible types of MKHs. This is joint work with M. Mars and J. Senovilla. 

Abstract: We discuss time quasi-periodic solutions to nonlinear Klein-Gordon equations on the torus in arbitrary dimensions. We will explain the result and the method, which is based on Anderson localization and algebraic geometry. 

Abstract: On the way towards a feasibility study of waveguide-based gravitational wave detection, the seminar will review the very basic calculations of interferometric gravitational wave detection within 3 different descriptions: 
- lightlike geodesics (TT gauge) 
- relativistic Maxwell equations (TT gauge) 
- laboratory frame considerations (LL gauge) 

Abstract: In string theory, our most developed theory of quantum gravity to date, one is interested in spacetimes of the form R^{1+3}_* K where K is some n-dimensional compact Ricci-flat manifold. In the first and simplest case considered by Kaluza and later Klein, K is the n-torus with the flat metric. An interesting question to ask is whether this solution to the Einstein equations, viewed as an initial value problem, is stable to small perturbations of the initial data. Motivated by this problem, I will outline the proof of stability in a restricted class of perturbations, and discuss the physical justification behind this restriction. Furthermore the resulting PDE system exhibits the weak-null condition, and I will discuss how it can be treated by generalising the proof of the non-linear stability of Minkowski spacetime given by Lindblad and Rodnianski.

Abstract: For metrics that are at least C^1,1 maximizing curves must be solutions of the geodesic equation and hence cannot change causal character: they must remain either timelike or null. This is no longer obvious for metrics of lower regularity and once the regularity drops below Lipschitz there are examples of "bubbling" metrics, for which maximizing causal curves may contain both timelike and null segments. We will present a recent result stating that Lipschitz regularity of the metric is sufficient for maximizing curves to have fixed causal character and show how this almost immediately gives a Lipschitz inextendibility result for timelike geodesically complete spacteimes. This is joint work with E. Ling.

Abstract: We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The role of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way we recover many fundamental results in greater generality, while at the same time clarifying the minimal requirements for and the interdependence of the basic building blocks of the theory. A main focus of this work is the introduction of synthetic curvature bounds, akin to the theory of Alexandrov and CAT(k)-spaces, based on triangle comparison. Applications include Lorentzian manifolds with metrics of low regularity, closed cone structures, and certain approaches to quantum gravity. This is joint work with Michael Kunzinger. Preprint: https://arxiv.org/abs/1711.08990

Abstract: After an introduction on gravitational waves and nonlinear effects in general, the talk will present the foundations of a new solution technique for the characteristic initial value problem of colliding plane gravitational waves. Assuming plane symmetry, the Einstein equations essentially reduce to the Ernst equation. In the course of the inverse scattering method this nonlinear PDE is tranlated first into an overdetermined linear system of differential equations and secondly into a Riemann-Hilbert problem. Ambiguities in this Riemann-Hilbert problem's solution lead to the construction of families of exact spacetimes generalising the proper solution to the initial value problem. Therefore the presented technique also serves as a solution generating technique. The method is exemplified by generalising the Szekeres class of colliding plane wave spacetimes. A new type of circularly polarised impulsive gravitational waves is identified within this generlisation.

Abstract: In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? The relational approach to physics suggests that all the features of a system —such as entanglement and superposition— are observer-dependent: what appears classical from our usual laboratory description might appear to be in a superposition, or entangled, from the point of view of such a quantum reference frame. In this work, we develop an operational framework for quantum theory to be applied within quantum reference frames. We find that, when reference frames are treated as quantum degrees of freedom, a more general transformation between reference frames has to be introduced. With this transformation we describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, which we explore in the case of ‘superposition of Galilean translations’ and ‘superposition of Galilean boosts’. In addition, we consider the situation when the reference frame moves in a ‘superposition of accelerations’, which leads us to extend the validity of the weak equivalence principle to quantum reference frames. Finally, this approach to quantum reference frames also has natural applications in defining the notion of the rest frame of a quantum system when it is in a superposition of momenta with respect to the laboratory frame of reference.

Abstract: We consider the limit a→∞ of the Kerr-de Sitter spacetime and analyze its global structure, with particular attention to its Killing horizons. This solution to Einstein's field equations with positive cosmological constant contains, apart from Λ, a unique free parameter which can be related to the angular momentum of one of its Killing horizons. A maximal extension of the (axis of the) spacetime is explicitly built. This is joint work with Marc Mars and Jose Senovilla.

Abstract: The recent discovery of gravitational waves by LIGO created renewed interest in the investigation of alternative gravitational detector designs, such as small scale resonant detectors. In this talk, it is explained how proposed small scale detectors can be tested by generating dynamical gravitational near fields with appropriate distributions of moving masses. This opens up the possibility to evaluate detector proposals very early in the development phase and may help to progress quickly in their development.

Abstract: After a review of known results on existence of periodic solutions of nonlinear wave equations, including Einstein equations, I will present a method based on analytic continuation to construct such solutions. In the Einstein case this involves complex valued tensor fields solving elliptic equations as a tool to obtain the real-valued Lorentzian solutions.

Abstract: The Milne model is the only cosmological vacuum solution to Einstein’s equations (with vanishing cosmological constant) that is known to be nonlinearly (future-) stable due to the work of Andersson-Moncrief. We present a first generalisation of this result to the nonvacuum case, namely to the Einstein-Vlasov system. In particular, we introduce a new idea to combine earlier approaches to control massive collisionless matter in cosmological spacetimes with a physically motivated estimate that is necessary to establish sufficient decay properties of the matter field. This is joint work with Lars Andersson (Golm).

Abstract: We introduce and discuss a notion of mass for static vacuum Einstein metrics with positive cosmological constant. In this context, we provide a positive mass statement as well s sharp area bounds for both cosmological horizons and black hole type horizons. In the first case, these area bounds represent the natural extension of a well known result by oucher, Gibbons and Horowitz, whereas for black hole type horizons they can be seen as the analogue of the celebrated Riemannian Penrose Inequality.
As an application, we deduce a uniqueness statement for the Schwarzschild--de Sitter static black hole.
(Joint work with S. Borghini).

Abstract: I discuss the canonical quantization of general relativity and Weyl-squared gravity. I present the classical and quantum constraints and discuss their similarities and differences.
I perform a semiclassical expansion and discuss the emergence of time for the two theories.
While in the first case semiclassical time has a scale and a shape part, in the second case it only has a shape part. I also address the relevance of these results for the general problem of understanding quantum gravity.
Ref.: C. Kiefer and B. Nikolic, J.Phys.Conf.Ser. 880 (2017) no.1, 012002 (open access) and references therein

Abstract: For a compact manifold $M^m$ equipped with a smooth fixed background Riemannian metric $\hat g$ we consider the space $\operatorname{Met}_{H^s(\hat g)}(M)$ of all Riemannian metrics of Sobolev class $H^s$ for real $s>\frac m2$ with respect to $\hat g$. The $L^2$-metric on $\operatorname{Met}_{C^\infty}(M)$ was considered by DeWitt, Ebin, Freed and Groisser, Gil-Medrano and Michor, Clarke. Sobolev metrics of integer order on $\operatorname{Met}_{C^\infty}(M)$ were considered in [M.Bauer, P.Harms, and P.W. Michor: Sobolev metrics on the manifold of all Riemannian metrics. J. Differential Geom., 94(2):187-208, 2013.]
In this talk we consider variants of these Sobolev metrics which include Sobolev metrics of any positive real (not integer) order $s>\frac m2$.
We derive the geodesic equations and show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping.
Based on collaborations with M.Bauer, M.Bruveris, P.Harms.

Abstract: Supercritical wave maps into spheres exhibit blowup via explicit self-similar solutions. I will present a recent stability result of the blowup profile which is valid in a large region of spacetime up to the Cauchy horizon of the singularity. This is joint work with P. Biernat (Bonn) and B. Schörkhuber (Vienna).

Abstract: The main purpose of this talk is to describe, by way of concrete examples, how the field of numerical relativity now contributes to our understanding of open questions in heavy-ion physics, gravitational collapse, and turbulence. I will begin by motivating these studies in terms of the physical systems that they are intended to clarify, and I will provide specific examples of how to describe these systems with numerical simulations of asymptotically AdS spacetimes in the fully non-linear regime of general relativity.

Abstract: In general relativity causal relations between any pair of events is uniquely determined by locally predefined variables – the distribution of matter-energy degrees of freedom in the events’ past light-cone. Under the assumption of locally predefined causal order, agents performing freely chosen local operations on an initially local quantum state cannot violate Bell inequalities. However, superposition of massive objects can effectively lead to “entanglement” in the temporal order between groups of local operations, enabling the violation of the inequalities. This shows that temporal orders between events can be “indefinite” in non-classical space-times.

Abstract: Informal presentation of the LIGO experimental setting

Abstract: The first confirmation of the theory of general relativity was given by the perihelion precession of the planet mercury in our own solar system. In recent decades, we have expanded our scope to many new extra-solar planetary systems, making use of rapidly improving observational techniques. This has opened up the possibility of observing the effects of general relativity in distant systems, giving additional confidence in our understanding of the universe.
I will present the findings of my bachelor thesis, concerning the impact of such a precession upon observable quantities in the system, as well as the methods used to extract them from the raw data.

Abstract: In order to improve QFT in 4 D we (HG and Raimar Wulkenhaar) studies models over quantized space-times. They become Matrix models, which share all interesting features of a QFT: A graphical description with Feynman rules, power counting dimension, regularisation and renormalisation, divergence of the perturbation series.- We report on models, where we can give exact non-perturbative formulae for all renormalised correlation functions. We describe a map, which projects these matrix correlation functions to Schwinger functions of an ordinary quantum field theory. The Schwinger 2-point functions satisfies in some models the Osterwalder-Schrader axioms.

Abstract: TBA

Abstract: I will show how to construct non-trivial, stationary black hole space-times with a singularity-free domain of outer communications,, solutions of Einstein-matter field equations with a negative cosmological constant.
Talk based on joint work with Erwann Delay and Paul Klinger, arXiv:1708.04947

Abstract: The majority of physicists wants to quantize gravity. To unify gravity and particle physics there is another possibility, a geometrization of particle physics. We will present some ideas in this direction. I will give some short overview on a simple model of rotating Dreibeins. This model has four types of stable topological solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number. Inspired by the silicon oil drop experiment of Yves Couder we follow the idea that a subquantum medium could influence classical solitons on their path and lead to quantum mechanics. Under this point of view we investigate the influence of a gravitational wave background on particles in circular motion. Based on joint work with Martin Suda.

Abstract: We show nonexistence of non-trivial solutions of the linearised near-horizon equations at the Kerr metric.

Abstract: The study of low regularity extensions of Lorentzian manifolds was initiated by Sbierski's 2015 paper on the C^0 inextendibility of Schwarzschild. The interest in such extensions arises from their connection with the strong cosmic censorship conjecture, i.e. the question of whether maximal globally hyperbolic developments can be extended. Here, I will review Sbierski's proof, focusing on extensions across the r=0 singularity, and present some new results concerning C^0 extensions of inhomogeneous spacetimes.

Abstract: A notion of "circularity" is proposed in geometric terms based on symmetry considerations. The main geometric object turns out to be closely related to the extrinsic curvature of the family of hypersurfaces defined by constant angular momentum. The solution of the geodesic equation in this setting can then be reduced to a single 2nd-order pde involving the mean curvature of these hypersurfaces. Their stability against linear perturbations can be reduced to a system of two odes having the structure of a damped harmonic oscillator. Even in the very well-known setting of time-independent spacetimes, this angular-momentum based approach has some advantages over the more conventional one based on an effective potential. However its true potential lies in a time-dependent setting, where the conventional approach cannot be applied. Some examples are given.

Abstract: The interest in the quantum null energy condition (QNEC), introduced by Bousso et al in 2015 is twofold: on the one hand, classical energy conditions can be violated in quantum theories, whereas QNEC is conjectured to hold in classical and quantum theories. On the other hand, there exist two proofs for QNEC, one for free field theories and one for quantum field theories with a holographic gravity dual. I review the holographic proof, which relies on geometric properties of Anti-de Sitter, and point out possible loopholes (at least in our understanding of the proof). In the end I will show our numerical holographic setup and results from gravitational shock wave collisions that not only violate the null energy condition but appear to violate also QNEC.

Abstract: The anti-de Sitter (AdS) space is of great interest in contemporary theoretical physics due to the AdS/CFT correspondence. However, the question of stability of AdS space is unanswered till now. After giving the motivation for studies of asymptotically AdS spaces, I will review the AdS instability problem. This will include: evidence for instability of AdS space, existence and properties of time-periodic solutions, and finally the resonant approximation. If time permits I will comment on other asymptotically AdS solutions. Along with the results, I will give details of methods relevant to the topic.

Abstract: In the first part of the talk we try to come up with some basic notions about the subject as well as Black hole formation, explaining some details of the whole subject on GR and also why we have three different assumptions or ans\"atze for axion-dilaton system in type IIB String Theory. We then would like to study the gravitational collapse of the axion-dilaton system suggested by IIB in dimensions ranging from four to ten. We would also like to extend the previous analysis in the literature concerning the role played by the global SL(2, R) symmetry, evaluating the Choptuik exponents for different elliptic, parabolic and hyperbolic cases. Eventually we describe some of the open questions for two other assumptions and future directions. This talk is based on arXiv:1108.0078 (published in CQG) and 1307.1378,gr ( published in JCAP) in collaboration with my former supervisor Prof. Luis.Alvarez-Gaume and some works in progress.

Abstract: A burst of gravitational radiation passing through an arrangement of freely falling test masses far from the source will cause a permanent displacement of the masses, called the "gravitational memory''. It has recently been found that this memory is closely related to the change in the so called "super-translation'' charge carried by the spacetime, where "super-translations'' here refer to an unexpected enlargement of the asymptotic symmetries of general relativity beyond the expected asymptotic Poincare-transformations, known already since the work of Bondi et al. in the early 60s (no relation with "supersymmetry''). I will describe these concepts from an intuitive perspective and point out that super-translations, as well as gravitational memory, are a phenomenon that is unique to relativity in 3+1, but not higher, dimensions. I close the talk by outlining the relation between these results and recent proposals connecting super translations to the Information Loss Paradox concerning Hawking-evaporating black holes.

Abstract: Black hole entropy S is one of the most fascinating issues in contemporary physics, as one does not yet strictly know what are the degrees of freedom at the fundamental microlevel, nor where are they located precisely. In addition, extremal black holes, in contrast to non-extremal ones, present a conundrum, as there are two mutually inconsistent results for the entropy of extremal black holes. There is the usual Bekenstein-Hawking S = A/4 value, where A is the horizon area, obtained from string theory and other methods, and there is the prescription S = 0 obtained from Euclidean arguments. In order to better understand black hole entropy in its generality, we exploit a matter based framework and use a thermodynamic approach for an electrically charged thin shell. We find the entropy function for such a system. We then take the shell radius into its gravitational radius (or horizon) limit. We show that: (i) For a non-extremal shell the gravitational radius limit yields S=A/4. The contribution to the entropy comes from the pressure. (ii) For an extremal shell the calculations are very subtle and interesting. The horizon limit gives an entropy which is a function of the horizon area A alone, S(A), but the precise functional form depends on how we set the initial shell. The values 0 and A/4 are certainly possible values for the extremal black hole entropy. This formalism clearly shows that non-extremal and extremal black holes are different objects. In addition, the formalism suggests that for non-extremal black holes all possible degrees of freedom are excited, whereas in extremal black holes, in general, only a fraction of those degrees of freedom manifest themselves. We conjecture that for extremal black holes the entropy S is restricted to the interval between 0 and A/4. Since an extremal shell has zero pressure, the contribution to the entropy comes from the shell's electricity. (iii) There is yet another possibility: to take the extremal limit concomitantly with the gravitational radius limit. In this case, and contrary to the two previous cases, remarkably, both the pressure and the electricity on the shell contribute to the entropy to give S=A/4.

Abstract: For given initial data to Einstein's field equations, one can find a spacetime solving these equations, and one can do so in a unique way (up to isometries) if one assumes the spacetime to be maximal globally hyperbolic. Both statements were proven by Choquet-Bruhat and Geroch in the 1950s and 60s. When dropping the additional condition of global hyperbolicity, it is an open question whether one can extend this spacetime, possibly in a non-unique way. Strong Cosmic Censorship conjectures that no such extension exists, at least not for generic initial data. In my talk, I focus on spacetimes where the initial data is symmetric under the action of a three-dimensional Lie group (a so-called Bianchi spacetime) and the stress-energy tensor is that of vacuum or a perfect fluid. I present results proving the Strong Cosmic Censorship conjecture for orthogonal Bianchi class B spacetimes and explore in more detail the asymptotic behaviour towards the initial singularity.

Abstract: Of particular relevance for an understanding of the low-temperature properties of a quantum system is the excitation spectrum. With the exception of exactly solvable models in one dimension, rigorous results on its structure are lacking and one has to resort to adhoc approximations to make predictions. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such systems are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior of the system.

Abstract: As Einstein's equations tell us that all energy is a source of gravity, light must gravitate. However, because changes of the gravitational field propagate with the speed of light, the gravitational effect of light differs significantly from that of massive objects. In particular, the gravitational force induced by a laser pulse is due only to its creation and annihilation and decays with the inverse of the distance to the pulse. We can expect the gravitational field of light to be extremely weak. However, the properties of light are premises in the foundations of modern physics: they were used to derive special and general relativity and are the basis of the concept of time and causality in many alternative models. Studying the back-reaction of light on the gravitational field could give new fundamental insights to our understanding of space and time as well as classical and quantum gravity. In this talk, a brief overview is given of the gravitational field of laser pulses in the framework of linearized Einstein gravity. A glimpse is caught of the gravitational interaction of two single photons, which turns out to depend on the degree of their polarization entanglement.

Abstract: In the process of gravitational collapse, singularities may form, which are either covered by trapped surfaces (black holes) or visible to faraway observers (naked singularities). In this talk, I will present four results with regard to gravitational collapse for Einstein vacuum equation. The first is a simplified approach to Christodoulou’s monumental result which showed that trapped surfaces can form dynamically by the focusing of gravitational waves from past null infinity. We extend the methods of Klainerman-Rodnianski, who gave a simplified proof of this result in a finite region. The second result extends the theorem of Christodoulou by allowing for weaker initial data but still guaranteeing that a trapped surface forms in the causal domain. In particular, we show that a trapped surface can form dynamically from initial data which is merely large in a scale-invariant way. The second result is obtained jointly with Jonathan Luk. The third result addressed the following questions: Can a ``black hole’’ emerge from a point? Can we find the boundary (apparent horizon) of a ``black hole’’ region? The fourth result extends Christodoulou’s famous example on formation of naked singularity for Einstein-scalar field system under spherical symmetry. With numerical and analytic tools, we generalize Christodoulou’s result and construct an example of naked singularity formation for Einstein vacuum equation in higher dimension. The fourth result is obtained jointly with Xuefeng Zhang.

Abstract: In this talk I will give an overview of Friedrich’s construction of a regular asymptotic initial value problem at spatial infinity and the open questions related to it. In particular, I will show how this framework can be used to identify initial data sets for the vacuum Einstein field equations which should lead to spacetimes not satisfying the peeling behaviour. This is research in collaboration with Edgar Gasperin.

Abstract: First, I will present the Yang-Mills equations on arbitrary fixed curved space-times, valued in the Lie algebra associated to any arbitrary Lie group. Thereafter, I will expose recent results with Dietrich Häfner concerning the Yang-Mills fields valued in the Lie algebra su(2) associated to the Lie group SU(2), propagating on the Schwarzschild black hole. We assume that the initial data are spherically symmetric, satisfying a certain Ansatz and have small energy, which excludes the stationary solutions which do not decay. We then prove uniform decay estimates in the entire exterior region of the black hole, including the event horizon, for gauge invariant norms on the Yang-Mills curvature generated from such initial data, including the $ L^\infty $ norm of the so-called middle components. This is done by proving in this setting, a Morawetz type estimate that is stronger than the one assumed in previous work, without passing through the scalar wave equation on the Yang-Mills curvature, using the Yang-Mills equations directly.

Abstract: In this talk we discuss the dynamics of continua on differentiable manifolds. We present a covariant derivation of equations of motion, viewing motion as a curve in the infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies; residual stress results from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two- dimensional curved annulus embedded in a sphere. Based on a joint work with Raz Kupferman and Reuven Segev.

Abstract: Motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, I will discuss nonlinear gravitational perturbations of maximally symmetric solutions of vacuum Einstein equations in general and the case of AdS in particular. I will present the evidence that, similarly to the self-gravitating scalar field at spherical symmetry, the negative cosmological constant allows for the existence of globally regular, asymptotically AdS, time-periodic solutions of vacuum Einstein equations that bifurcate from linear eigenfrequencies of AdS. Interestingly, preliminary results indicate that the number of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of this eigenfrequency. The talk will be based on the recent preprint arxiv.org/abs/1701.07804

Abstract: It is well-known that spatial infinity cannot be represented as a regular point due to blow-ups of the Weyl tensor whenever the ADM mass is non-zero. Because of this, the construction of vacuum spacetimes which admit a smooth past and future null infinity turns out to be a rather intricate problem. An approach which avoids these blow-ups is a cylinder representation of spatial infinity. However, for generic initial data the solutions will pick up log-terms at the critical sets where the cylinder "touches" null infinity. The goal of this talk is to set up an asymptotic initial value problem with data at past null infinity and to derive necessary conditions for the smoothness of these critical sets.

Abstract: I will first describe the Schwarzschild-Anti-de Sitter spacetime and the geometrical properties that makes it interesting to look at when studying hyperbolic equations. I will then present the Dirac equation in this spacetime and investigate quickly the Cauchy problem. The solution is then analyzed from the point of view of scattering theory. First, I will look at this solution in the asymptotic region of the spacetime and give a result about the asymptotic completeness and the asymptotic velocity. Then, I will look at local properties of these fields for large time and give a lower bound on the local energy decay using the construction of exponentially accurate quasimodes. I will then present some tools to obtain an upper bound will then be such as the resonances and the WKB solutions that should allow to localize these resonances.

Abstract: In my talk, I will present a new representation of loop quantum gravity with spinors as the fundamental configuration variables. I will show, in particular, that the discrete loop quantum gravity spin degrees of freedom (on a spin-network) can be related to classical surface degrees of freedom of the gravitational field on a null surface. The approach is based on the covariant Hamiltonian formulation for a manifold with (inner) null boundaries. The underlying action consists of the the self-dual action in the bulk plus an additional boundary term. The boundary term is required, because otherwise the action is not functionally differentiable. On the null boundary, the most natural such boundary term can be written in terms of spinors. The resulting canonically conjugate variables on the null surface are a spinor and a spinor-valued two-surface density. The quantisation of both the constraints (reality conditions) and the boundary symplectic structure reproduces the loop quantum gravity Hilbert space in the spinorial representation. The talk is based on the papers [arXiv:1611.02784, arXiv:1604.07428, arXiv:1107.5002].

Abstract: Full general relativity is almost certainly 'chaotic'. I will argue that this entails a notion of nonintegrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, is likely to possesses neither differentiable Dirac observables nor a reduced phase space. The standard notion of observable then has to be extended to include non-differentiable observables. This has severe repercussions as such observables cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. Nevertheless, in certain cases, one can explicitly quantize such systems. By means of toy models, I will discuss general challenges and some surprising consequences for the quantum theory of nonintegrable constrained systems which presumably will also appear in canonical quantum gravity. Based on arXiv:1602.03237, 1508.01947.

Abstract: I will present an elementary argument that one can shield linearised gravitational fields using linearised gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in shielding or gluing constructions for the linearised metric.

Abstract: In this talk I will review the state of the art in the theoretical and experimental study of analog models of quantum field theories in flat, curved, or time-dependent backgrounds using condensed matter and optical systems. In the first part, I will focus on the theory of the stimulated and spontaneous Hawking emission of phonons in flowing fluids of ultracold atoms and of photons in semiconductor microcavities and I will outline the state of the art of experimental investigations. In the second part, I will introduce analogs of two-level emitters coupled to the quantum field and I will present recent works on the observable consequences of Casimir physics and of Ginzburg radiation processes for moving emitters. I will conclude with an outline of more speculative investigations in the direction of highlighting the back-reaction effect of Hawking emission onto a black hole horizon.

Abstract: In this talk I report on work in progress on Bowen-York type initial data with positive cosmological constant.

Abstract: We will describe how the theory of entanglement provides a novel language for describing quantum many body systems. We will demonstrate how the ensuing quantum tensor networks allow for the classification of topological quantum phases of matter.

Abstract: The non-linear stability problem for Kerr black holes is still very much open. In my talk, I explain the conjecture, lay out the strategy to prove it and focus on the base step: mode stability for the Kerr black hole.

Abstract: The fact that collisional energy of two particles near Kerr black holes can be arbitrary high, has been broadly discussed in the literature in recent few years. However, it has also been noticed that this phenomenon is not significant for distant observers. During my talk I will firstly discuss these two issues, and then move to the analysis of collisions on the innermost stable circular orbit. I will focus on the lower bounds of energy of such collisons in extreme-Kerr limit.

Abstract: I will review in this talk the commutator theory for the transport equation on curved spacetimes, and suggest, as an application, the derivation of an integrated energy decay for massless Vlasov fields on Kerr black holes. This work is a direct application of the work by Andersson and Blue (Ann. Math. 15) for the wave equation, combined with the commutator theory for the transport equation developed by Fajman, Joudioux and Smulevici. This is an ongoing work in collaboration with Pieter Blue.

Abstract: The first fact I will discuss is that Hawking radiation is primarily not an effect of black-hole physics, or even General Relativity, but of a more general character that points towards a simple solution of the so-called black hole information paradox. The second fact concerns the difference between ordinary thermal and Hawking radiation.

Abstract: Newton-Cartan geometry is a geometric, covariant description of non-relativistic gravity, akin to General Relativity. Recently, it has seen a renewed interest in the context of condensed matter physics and applications of holography to condensed matter systems. In this talk, I will briefly describe the motivation for this renewed interest. I will then outline how Newton-Cartan gravity can be conveniently described as a gauging of a suitable extension of the Galilei algebra of non-relativistic space-time symmetries. Finally, I will show how this gauging procedure can be applied to yield extensions of Newton-Cartan geometry that implement conformal symmetry and supersymmetry.

Abstract: The notion of "soft hair" refers to zero energy excitations in the near horizon region of black holes or cosmologies, advocated by Hawking, Perry and Strominger. I review recent results on soft hair in three spacetime dimensions. In particular, I focus on the near horizon symmetry algebra, which turns out to be surprisingly simple, namely infinite copies of the Heisenberg algebra. The results are universal (in a sense that I shall make precise) and could generalize to higher dimensions. Talk based on arXiv papers 1603.04824, 1607.00009, 1607.05360.

Abstract: Higher-spin gauge theories provide interesting, highly symmetric extensions of gravity. The only known interacting higher-spin gauge theories are the so-called Vasiliev theories. I will give an introduction to these theories and the unfolding formalism on which they are based. I will also discuss recent results which point out that the extraction of concrete equations of motion not only poses a technical, but also a conceptual challenge.

Abstract: Arguably, the most important milestone of Quantum Field Theory in curved spacetime is the discovery by Stephen Hawking that black holes should evaporate by emitting a Planckian spectrum of particles, the so-called Hawking radiation. With a similar derivation, Bill Unruh postulated that accelerated observers in empty space should perceive a thermal bath of particles with temperature proportional to their acceleration, the so-called Unruh effect. It seems clear that, for an observer following an arbitrary trajectory outside a black hole, these two effect must be present together. But, how do they combine to give the observer's net particle perception? In this talk we will address this question, within a restricted but conceptually clear framework, by using the so-called effective-temperature function. Far from just getting a set of concrete quantitative results for different trajectories of the observer, we will obtain general results which are clearly interpretable in terms of well-known physical phenomena. Furthermore, these results will let us address some interesting questions: Which part of the radiation perceived can be assigned to Hawking radiation and which to the Unruh effect? Can these two effects interfere destructively? Does always the Unruh temperature scale with the proper acceleration of the observer? Is it strictly necessary to form a horizon in order to have Hawking radiation emitted? Can Hawking radiation make a test particle to float nearby a black hole due to radiation pressure?

Abstract: After an introduction to gluing constructions for initial data in theories with constraints, I will describe the Carlotto-Schoen gluing construction, which allows to screen away gravitation using the gravitational field.

Abstract: Quantum theory and general relativity are considered the two pillars of modern physics. Their predictions are verified with spectacular precision on scales covering several orders of magnitude. Despite their success in describing nature, a unique framework reconciling these two theories is still missing. In this talk we will present a modified version of a Mach-Zehnder interferometer, capable of realizing the first table-top experiments probing jointly the quantum superposition principle and the mass-energy equivalence principle for single photons. The novel gravitational effects to be tested in this project arise when a single photon is travelling in a superposition along two paths located at different heights above earth and which are then brought to interfere. Due to the Shapiro delay, the travel time of a photon depends on the altitude of its path above earth. For the time dilation comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations gravity will induce a relative phase, shifting the interference pattern. As required by quantum complementarity principle, there is a trade-off between the possibility to observe interference and the amount of information about the photon's path, in our proposed experiment available from the arrival time of the photon.

Abstract: For freely floating self-gravitating bodies the boundary conditions on physical grounds are: the vanishing of the normal stress at the boundary for all times. We expect that these conditions together with initial data determine a unique solution of the evolution equations. However, if the density of the matter at the surface of the body is positive, further "transition conditions" are needed to imply sufficient differentiability of the solution inside and outside the body. I will discuss the origin of these conditions first for a simple model problem and then for self-gravitating bodies in Newton's and Einstein's theory of gravity.

Abstract: I will review the state of the art in atom and macromolecule interferometry to stimulate discussions on quantum physics, gravity and cosmology. A large part of the talk will be dedicated to open questions the correct answers to which I do not know at all: Do wave functions collapse ‘objectively’ when objects become massive and delocalized over large periods of time? How would this influence the temperature of the universe? Why does mass do if nobody watches? How could the universe not watch at all? How will the gravitational warp of space-time modify the linearity of Schrödinger’s wave mechanics for very massive and highly delocalized clusters? Is there any chance of observing fluctuations of space time in matter-wave interferometry? Can we use nanoparticle matter-waves for gravitational wave detection? What do we learn about the weak equivalence principle and possible modifications of the standard model when we compare the matter-wave fringe shift of macromolecules and single atoms in free fall? Which quantum particle is best suited for probing Non-Newtonian gravity at short distances? Can matter-wave interferometry serve as a detector for dark matter at low energy? What is needed for serious experimental tests?

Abstract: Ever since Stephen Hawking discovered that black holes emit radiation, the physics community has been trying to accommodate the effects of this phenomenon. One of its consequences is the so-called information paradox. This paradox arises once a black hole evaporates through the emission of Hawking radiation, when those parts of the radiation that left the black hole can't be described as entangled with the hole anymore. While the theory assumes a pure initial state and hence full information about the particles in the hole and those emitted, information is lost once the hole is gone. This implies a loss of unitarity. Several ways to avoid this prospect are conceivable but few of them seem favourable. One such resort is the supposition that Hawking radiation has been treated too superficially since higher order corrections of its state are usually neglected. Their contribution could destroy the particles' entanglement, thus resolving the entire paradox. This work investigates Samir Mathur's research, who tried to disprove this proposal. Mathur shows that as long as these corrections to the Hawking state are assumed to be small, they cannot affect the first order entropy in a decisive way. Mathur's assumptions are examined in greater detail and his results are revised to conform to Hawking's results. We refine the entropy inequalities he proposed and attempt to directly compute the entanglement entropy of the Hawking radiation.

Abstract: Numerical studies of inhomogeneous singularities have provided strong evidence for the BKL picture of generically spacelike and oscillatory singularities. However the "local" part of the conjecture (which claims that the dynamics is asymptotically given by a spatially homogeneous model at each point) seems to break down at isolated points, where so-called spikes form, i.e. spatial derivatives become non-negligible, at least intermittently. This behavior can also be seen in explicit symmetric models, which have been proposed as the building blocks for the fully inhomogeneous case. I will introduce the dynamical systems formulation of the BKL conjecture introduced by Uggla et al. and the role played by the explicit spike solutions of Lim. These aim to give a complete description of the dynamics close to spacelike singularities, including the formation and resolution of spikes.

Abstract: Zero rest-mass fields (the electromagnetic field and the linearised gravitational field) prop- agating on flat space and their corresponding Newman-Penrose constants are studied near spatial infinity. The aim of the analysis made in this article is to clarify the correspondence between data for the field on a spacelike hypersurface and their corresponding Newman- Penrose constants at future and past null infinity. To do so, the framework of the cylinder at spatial infinity is employed to show that, expanding the initial data as in terms spherical har- monics and powers of the geodesic spatial distance ρ to spatial infinity, the Newman-Penrose constants correspond to the data for the highest possible spherical harmonic at fixed order in ρ. As a by product of this analysis, it is shown that the electromagnetic constants at future and past null infinity are related as they correspond to the same portion of initial data. Moreover, it is shown that, this is true for generic data (not necessarily time-symmetric) and the mechanism responsible for this identification, encoded in the evolution and constraint equations, is discussed.

Abstract: We consider the Einstein-dust equations with positive cosmological constant $\lambda$ onmanifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the Einstein-$\lambda$-dust equations on $S$ contains an open (in terms of suitable Sobolev norms) subset of data which develop into solutions that admit at future time-like infinity a space-like conformal boundary ${\cal J}^+$ that is $C^{\infty}$ if the data are of class $C^{\infty}$ and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on ${\cal J}^+$. These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.

Abstract: This is an overview talk on the topic. It starts with the early pioneering experiments by Pound and Rebka and by Colella, Overhauser and Werner that demonstrate the effect of the gravitational potential on the frequency of a photon and on quantum interference fringes in a neutron interferometer, respectively.
The latter represents the first experiment that required the use of both Planck’s constant and Newton’s constant (via earth’s acceleration g) to describe the observed interference fringes. Over the following decades, modern quantum physics added new tools and allowed to significantly expand the available quantum experiments that test the effects of weak gravitational fields, including atomic fountains (pioneered by Kasevich and Chu), lab-¬‐based atomic clock tests of the gravitational red shift or the demonstration of gravitationally bound states of cold neutrons. The last few years have seen a renewed interest and a significant increase of experiments (and experimental proposals) to explore the interface between quantum physics and gravity. On the one hand, quantum optics and cold atom experiments have been pushing the sensitivity of measurements of space and time to unprecedented regimes: squeezed states of light have been shown to increase the sensitivity of interferometric gravitational wave detectors, atomic clocks have reached a precision to detect mm-¬‐scale displacements in earth's gravitational field, and atomic fountain experiments can measure Newton’s constant with a precision comparable to the best known values to date (100ppm). Other proposed applications of cold quantum gases and atomic clocks include the measurement of gravitational waves and demonstrations of quantum field theory in curved space-¬‐time. On the other hand, the fast progress in macroscopic quantum experiments may soon allow
to study large quantum superposition states involving clocks or increasingly massive objects. The latter could open a completely new regime of experiments in which the source mass character of the quantum system starts to play a role. This is reminiscent of Feynman’s proposal at the 1957 Chapel Hill Conference on the generation of entanglement through gravitational interaction.

Abstract: The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. I will discuss the memory effect for a general, spatially flat FLRW cosmology by considering the radiation associated with emission events involving particle-like sources. Talk based on joint work with Alexander Tolish arxiv.org/abs/1606.04894.

Abstract: Parametrized field theories provide interesting examples of relatively simple diff-invariant systems, which can be then used as good toy models to understand some subtle features of General Relativity. In this talk, relying on the space of embeddings, I will explain some interesting aspects of the parametrized electromagnetic field, as it is one of the simplest models with gauge symmetries. In particular I will focus on how its primary constraint submanifold can be divided into sectors where different Hamiltonian dynamics take place, and show how the Gauss law comes into play (spoiler alert, it is not a constraint).

Abstract: We discuss the behavior of (classical) and quantum matter in impulsive pp-Yang-Mills fields employing nonlinear generalized functions.

Abstract: In this talk we illustrate a method that can be employed to describe qualitative properties of solutions to relevant geometric PDE's. In particular, we present some applications to the study of static metrics in general relativity. In this context, our method produces monotonicity formulas, from which sharp geometric inequalities can be deduced, whose equality case characterizes the model solutions.The results are obtained in collaboration with V. Agostiniani and S. Borghini.

Abstract: The Lagrange densities for metrics give Euler-Lagrange expressions which transform as tensor densities and are symmetric and divergence-free. This, together with requiring the tensor density to depend on only up to the second derivative of the metric, allowed Lovelock to find a general dimension-dependent form of such tensorial quantities. I will go through the derivation of his results in this matter. At the end I will also show that for any such divergence-free, symmetric tensor density there exists an associated L-degenerate Lagrange density.

Abstract: I will discuss several aspects of scattering theory in linear dispersive wave equations where the time derivative part is modified by a non-homogeneous background flow. The original motivation of this work is the analogy discovered by Unruh between sound propagating in a moving fluid and radiation around a black hole. In such setups, dispersive effect allow for new wave solutions with negative energy. I will describe how these solutions can be produced by linear conversion, their link with the Hawking effect, and several types of instabilities they give rise to.

Abstract: I shall start with some remarks on Ernst Mach (+1916), who spent many years at the University in Prague and at the Vienna University. I briefly recall his and Einstein's ideas on the origin of inertia and their influence on the construction of general relativity. I mention the direct experiment verifying relativistic dragging/gravitomagnetic effects - the Gravity Probe B; the results were summarized only recently. I shall then turn to several specific general-relativistic problems illustrating the gravitomagnetic effects: the dragging of particles and fields around a rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, linear dragging in a static situation, and the way how Mach's principle can be formulated in cosmology. A more detailed discussion will be devoted to the dragging effects by rotating gravitational waves.

Abstract: On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) detected a gravitational-wave (GW) transient (GW150914). We characterise the properties of the source and its parameters with Bayesian parameter estimation algorithms using waveform models that describe GWs emitted from binary black holes in general relativity. In addition, we compare these models against a set of numerical relativity (NR) waveforms in the vicinity of GW150914. Simplifications are used in the construction of some waveform models, such as restriction to spins aligned with the orbital angular momentum, no inclusion of higher harmonics in the GW radiation, no modeling of eccentricity and the use of effective parameters to describe spin precession. In contrast, NR waveforms provide us with a high fidelity representation of the "true" waveform modulo small numerical errors. We discuss where in the parameter space the above modeling assumptions lead to noticeable biases in recovered parameters.

Abstract: I will present recent results obtained in collaboration with D. Fajman and J. Joudioux concerning the study of relativistic kinetic equations via techniques inspired by the traditional vector field method of Klainerman. In the second part of my talk, I will give some applications to systems of relativistic transport equations coupled to wave equations, such as the Vlasov-Nordström system.

Abstract: The Vlasov-Monge-Ampere model, based on optimal transport ideas, is an approximate model for classical (Newtonian) gravitation, closely related to the Zeldovich model in Cosmology. A derivation will be proposed, based on a double application of large deviation principles, from the very elementary stochastic model of a Brownian point cloud without interactions.

Abstract: It is well known that the nodal set of solutions to semi-elliptic Dirac equations on closed Riemannian surfaces is discrete. We will derive an estimate on the nodal set of eigenspinors of the classical Dirac operator, twistor spinors, solutions to a nonlinear Dirac equation and eigenspinors of twisted Dirac operators that arise in quantum field theory. Moreover, we will point out geometric applications of our results.

Abstract: We show how certain microlocal analysis methods, already well-developed for the study of conventional Schrödinger eigenvalue problems, can be extended to apply to the (mini-superspace) Wheeler-DeWitt equation for the quantized Bianchi IX (or ‘Mixmaster’) cosmological model. We use the methods to construct smooth, globally defined asymptotic expansions, for both ‘ground’ and ‘excited state’ wave functions, on the Mixmaster mini-superspace. A crucial step in this extension involves handling the fact that, for spatially closed universe models, all of the relevant eigenvalues to the Wheeler-DeWitt operator must vanish identically-̶̶̶̶-̶ a sharp contrast to the situation normally arising for Schrödinger operators. We then briefly review an expansive, ongoing program to further extend the scope of such microlocal methods to encompass a class of interacting, bosonic quantum field theories and conclude with a discussion of the feasibility of applying this ‘Euclidean-signature semi-classical’ quantization program to the Einstein equations themselves ̶̶ ̶ in the general, non-symmetric case ̶ ̶ by exploiting certain established geometric results such as the positive action theorem.

Abstract: The Einstein-Vlasov system describes a large collection of collissionless particles interacting via the mean gravitational field, where gravity is modeled by general relativity. Here we present numerical solutions of these equations which are far-from spherically symmetric in the sense that the particle distributions take flattened and toroidal shapes, and the solutions have non-zero net angular momentum. In addition, certain families of solutions are found to contain ergoregions. This talk will include a discussion of the properties of the solutions obtained as well as the numerical methods.

Abstract: The commonly introduced description of electromagnetism in curved spacetime is concise and elegant but not particularly useful when describing materials of spatially dependent permittivity $\epsilon$. Thus, discussions of waveguides are typically limited to classical electromagnetism. In this talk, I will work towards a description of electromagnetism in curved spacetime that can be useful to discuss planar waveguides in a weak gravitational field while highlighting the difficulties in notation and convention that arise in the interdisciplinary context.

Abstract: I will discuss a family of topologically non-trivial linearized gravitational field configurations based on the Robinson congruence.

Abstract: Hermann and Humbert define a concept of mass associated with a class of 2nd order partial differential operators, which can be viewed as a generalized ADM mass and for which they prove a number of interesting properties.

Abstract: In this talk I will present recent results on blowup for wave equations with focusing power nonlinearities in odd space dimensions d \geq 3. It will be shown that in all criticality regimes open sets of radial initial data can be constructed such that the corresponding solution blows up in finite time and converges to the ODE blowup solution locally around the origin.

Abstract: Ultra cold quantum gases are an ideal system to probe many body physics and quantum fields. In this talk I will give an overview of the different possibilities and what we were able to learn about many body systems and their underlying quantum description.

Abstract: I first give an introduction to higher-spin gauge theories. I will discuss the free theory, and the difficulties that arise when one tries to introduce interactions and how they can be overcome. Finally I discuss asymptotic symmetries of higher-spin theories on AdS_3 and their role in the higher-spin AdS/CFT correspondence.

Abstract: Neutron stars mergers are among the strongest sources of gravitational waves and among the main targets for ground-based gravitational-wave interferometers Advanced LIGO and Virgo. The observation of these events in the gravitational-wave window can provide us with unique information on neutron stars' masses, radii, and spins, including the possibility to set the strongest constraints on the unknown equation-of-state of matter at supranuclear densities. However, a crucial and necessary step for gravitational-wave observations is the precise knowledge of the dynamics of the sources and of the emitted waveforms. I will talk about recent developments in the modeling of gravitational waves from neutron star mergers using numerical simulations in general relativity.

Abstract: Massless collisionless matter is described in general relativity by the massless Einstein–Vlasov system. I will present a proof that for smooth asymptotically flat Cauchy data for this system which is sufficiently close, in a suitable sense, to the trivial solution, Minkowski space, the resulting maximal development exists globally in time and asymptotically decays appropriately. By appealing to the corresponding result for the vacuum Einstein equations, a monumental result first obtained by Christodoulou–Klainerman in the early ’90s, theproof reduces to a semi-global problem. A key step is to estimate certain Jacobi fields on the mass shell, a submanifold of the tangent bundle of the spacetime endowed with the Sasaki metric.

Abstract: The Einstein flow with vanishing cosmological constant is known to be sensitive to the spatial topology of the spacetime. It is generally believed that initial data with positive curvature has a maximal development which is geodesically incomplete in both time directions, while the development of (certain) initial data with negative spatial curvature has one expanding, complete direction. Except for a few results which concern symmetric solutions or a neighborhood of explicit solutions, this behavior is not rigorously understood. Considering the case of 2+1-dimensional gravity this problem is more accessible, since the classification of closed surfaces without boundary restricts the possible topologies and leaves essentially three cases to study: the sphere, the torus and hyperbolic surfaces. In the talk we present a construction of expanding future complete solutions for all topologies, which - for some cases - require a non-vanishing energy-momentum tensor. This certainly contradicts the initially conjectured behavior. Moreover, the construction requires a certain asymptotic behavior of the energy density, which - as we show - is realized by matter models describing massive particles such as the Einstein-Vlasov system, but fails for massless matter models. Therefore, in 2+1-gravity, future completeness - independent of the spatial topology - is an effect caused by the mass of the individual particles. We discuss a proof for the nonlinear stability of those solutions for the cases of non-negative curvature, which implies that this is a robust phenomenon.

Abstract: The postulate of causality is among the most fundamental principles of physics. In relativity theory it is straightforward to implement, as the Lorentzian metric induces a partial order relation between the events. On the other hand, the study of causality for quantum objects --- which are inherently non-local --- is still incomplete. Basing on a recent article (arXiv:1510.06386), we will present a rigorous notion of causality for nonlocal objects, modelled by probability measures on a given spacetime. The work is embedded in the optimal transport theory and explores the borderland between mathematical relativity and measure theory. We will argue that the proposed definition captures an intuitive notion of causality for spread objects and show how various results on causality in quantum theory, aggregated around Hegerfeldt’s theorem, fit into our framework.

Abstract: In this talk the constraint equations for smooth spaces satisfying Einstein's equations will be considered. It is shown that, regardless whether the primary space is Riemannian or Lorentzian, the constraints can always be put into the form of an evolutionary system comprised either by a first order symmetric hyperbolic system and a parabolic equation or, alternatively, by a symmetrizable hyperbolic system subsided by an algebraic relation. The (local) existence and uniqueness of solutions to these evolutionary systems is also shown verifying thereby that the proposed evolutionary approach provides a viable alternative to the apparently unique conformal method.

Abstract: In this talk I will present a spectral decomposition of solutions to relativistic wave equations on a given Schwarzschild-black-hole background. To this end, the wave equation is Laplace-transformed which leads to a spatial differential equation with a complex parameter. This equation is treated in terms of a sophisticated Taylor series analysis. Thereby, all ingredients of the desired spectral decomposition arise explicitly, including quasi normal modes, quasi normal mode amplitudes and the jump along the branch cut. Finally, all contributions are put together to obtain via the inverse Laplace transformation the spectral decomposition in question.

Abstract: In this talk I will show how the asymptotic initial value problem for the conformal Einstein field equations, whereby one prescribes initial data on a spacelike hypersurface representing the conformal boundary, can be used to study various conformal aspects of the Schwarzschild-de Sitter spacetime. The analysis presented covers the subextremal, extremal and hyperextremal cases.

In my talk, I prove a no-theorem for static and axially symmetric black holes surrounded by matter. More precisely, I will show that external fields do not induce multipole moments in such black holes that could be read off at infinity. The key ingredients in the proof is the source integral formalism, which will be introduced as well. It allows to define quasi-locally for each region in the spacetime its contribution to the asymptotically defined total multipole moments of that spacetime.

Abstract: In general relativity, a self-gravitating system such as a binary star is not expected to display time-periodic dynamics, due to the emission of gravitational waves. In my lecture I will present a recent result that rules out the existence of genuinely time-periodic solutions to the Einstein equations, at least in the vacuum region far away from compact sources. I will discuss the relevance of the result to the final state conjecture, and elaborate on the proof which relies on novel uniqueness theorems for a class of ill-posed problems for geometric hyperbolic p.d.e.'s.

Abstract: As for the wave equation, the Vlasov equation admits commutators arising from the geometry. This allows standard PDE techniques, such as the vector fields method, to be applied to this geometric transport equation. In this talk, the relevant geometric structures of the Vlasov equation will be explained, and exploited to apply vector fields methods. The asymptotic behaviour of Vlasov fields, with data in some weighted Sobolev spaces, on flat space-time, can then be described using Klainerman-Sobolev inequalities. Applications to the massless and massive Vlasov-Nordström system are discussed in the last parts of the talk. In particular, a precise asymptotic behaviour for solutions of this system will be derived. This is a collaboration with D. Fajman (Vienna), and J. Smulevici (Orsay-Paris 11).

Abstract: Maximal (hyper)surfaces are sometimes referred to as relativistic strings or membranes. They are objects of considerable interest in relativity and string theory. However little is known about their long-time behavior. We discuss recent progresses in this regards.

Abstract: In this introductory talk I will start by explaining some basic properties of the Dirac operator on Riemannian and Lorentzian manifolds. I will revise the Atiyah-Singer index theorem and the Atiyah-Patodi-Singer index theorem for manifolds with boundary and discuss some applications. I will then discuss a recent result about the index of the Dirac operator on a globally hyperbolic spacetime and the relation to physics.

Abstract: I will discuss the steps of quantization of a simple cosmological model. Starting with the unimodular version of General Relativity the result will be an evolving wave function. There is no need for the commonly used frozen time formalism.

Abstract: A Bondi-type mass, associated with a cut of the conformal boundary of asymptotically de Sitter spacetimes is suggested. This is based on the integral of the Nester-Witten 2-form and the Witten-type positivity argument on a spacelike hypersurface intersecting the conformal boundary in the cut. It is shown that this integral (1.) can be finite only if the boundary value of the Witten spinor at the cut solves the 2-surface twistor equation, (2.) is positive if the matter fields satisfy the dominant energy condition on the spacelike hypersurface, and (3.) its vanishing is equivalent to the local de Sitter nature of the domain of dependence of the hypersurface. However, this integral gives a well defined notion of mass only in the presence of some extra structure. In particular, when the cut is non-contorted, the integral yields an invariant analogous to the Bondi mass, which is positive and has the rigidity.

Abstract: A spherically symmetric accretion model introduced by Bondi in 1952 belongs to classical textbook models of theoretical astrophysics. Its general relativistic version is due to Michel, who considered spherically symmetric, purely radial, stationary flow of perfect fluid in the Schwarzschild spacetime. Solutions of the Bondi-Michel flow are usually parametrized by fixing asymptotic values of the density and the speed of sound at infinity; they extend smoothly from infinity up to the horizon of the black hole (and below). In contrast to that, local solutions, that cannot be extended to infinity, were recently discovered in the cosmological context. They correspond to homoclinic orbits on phase diagrams of the radial velocity vs. radius (say). More surprisingly, they also appear in the standard Bondi-Michel model for polytropic fluids with polytropic exponents larger than 5/3. In this talk I will discuss recent results on the existence of those local, homoclinic solutions.

Abstract: Hawking radiation and particle creation by an expanding Universe are paradigmatic predictions of quantum field theory in curved spacetime. Although the theory is a few decades old, it still awaits experimental demonstration. At first sight, the effects predicted by the theory are too small to be measured in the laboratory. Therefore, current experimental efforts have been directed towards siumlating Hawking radiation and studying quantum particle creation in analogue spacetimes.

In this talk, I will present a proposal to test directly effects of quantum field theory in the Earth's spacetime using quantum technologies. Under certain circumstances, real spacetime distortions (such as gravitational waves) can produce observable effects in the state of phonons of a Bose-Einstein condensate. The sensitivity of the phononic field to the underlying spacetime can also be used to measure spacetime parameters such as the Schwarzschild radius of the Earth.

Abstract: In the first part of the talk we present a proof of the mass-angular momentum-charge inequality for multiple black holes (joint with Gilbert Weinstein). In the second part, new inequalities relating the size and angular momentum as well as size and charge of bodies is presented. Lastly, black hole existence results due to concentration of angular momentum and charge will be discussed.

Abstract: I will review the method and results of the elementary proof of positivity of the Trautman-Bondi mass of light-cones with complete generators in asymptotically Minkowskian space-times by P. T. Chruściel T.-T. Paetz and present the changes and our resulting formula for the Trautman-Bondi mass of light-cones with complete generators in asymptotically anti-de Sitter space-times.

Abstract: TBA

Abstract: We present a new approach to the study of asymptotically flat static metrics in general relativity. Our method works in every dimension and it is based on a conformal splitting technique, which has been previously applied by the authors to the study of the geometric aspects of classical potential theory. The results are obtained in collaboration with V. Agostiniani.

Abstract: The limit obtained when letting a free parameter of a spacetime approach a certain value is in general not unique, but depends on the choice of coordinates. This ambiguity led Geroch to formulate a definition of limits of a one-parameter family of spacetimes in 1969. We have come up with an application of Geroch’s definition, which makes it possible to see the limiting procedure in pictures. The general idea is to let the spacetime under consideration---if possible---be represented by a 1+1-dimensional surface reflecting its essential causal structure, and embed this surface in 2+1-dimensional anti-de Sitter space. With the help of a conformally compactified picture of adS3 the result is reminiscent of a Penrose diagram, with the difference that the picture will change as we vary the parameter. The examples considered here are two different limits obtained when letting the charge parameter e of a Reissner-Nordström black hole approach the mass m. The conformally compactified picture of adS3 and the embeddings of the black hole surfaces will be explained.

Abstract: The holographic principle was originally motivated by the desire to reconcile black hole evaporation with unitarity and found a concrete implementation in AdS/CFT. However, the way AdS/CFT works makes it logically possible that holography might work for non-unitary theories as well. Moreover, if holography is a true aspect of Nature then it must also work for non-AdS spacetimes. It is therefore of interest to pose the question in the title. I review recent progress on these issues, with particular focus on flat space holography.

Abstract: It is a classical observation that geodesic balls at points of positive scalar curvature contain more volume than a round ball in Euclidean space with the same surface area. In this talk, I will discuss the global effect of non-negative scalar curvature on isoperimetry in asymptotically flat manifolds.

Abstract: The two concepts in the title stand for two distinct quantum phenomena whose relation to one another is not obvious although they often occur together. Moreover, there is not a unique concept of superfluidity. In the talk I shall first comment on these general issues and then discuss a simple model involving a tunable random potential where some precise statements can be rigorously proved. The latter is joint work with M.Könenberg, T. Moser and R. Seiringer.

Abstract: I will review known classes of Einstein-Maxwell instantons, and present a new class of such solutions with lens-space topology.

Abstract: In this talk, I review properties of the so-called "deSitter spacetime", and some properties of quantum field theories that live on this spacetime. The investigation of such theories is highly relevant to cosmology, because deSitter space is thought to describe the earliest epoch of our universe, at least to some approximation. It is also interesting from a Mathematical viewpoint, because deSitter space is a space with maximal symmetry, making possible several explicit constructions and investigations that would be out of reach in quantum field theories on more general Lorentzian manifolds.

Abstract: In vacuum space-times with an isometry and with $\Lambda=0$, the Mars-Simon tensor (MST) has been introduced to provide a characterization of the Kerr-NUT-metrics. Moreover, it was used by Klainerman et al. to prove uniqueness of the Kerr black hole under certain restrictive hypotheses. Recently, Mars and Senovilla considered this tensor for arbitrary $\Lambda$, and they analyzed the family of metrics characterized by the vanishing of the MST. In this talk, we restrict attention to $\Lambda>0$-vacuum space-times which admit a smooth scri. In this setting we reconsider and extend their analysis from the point of view of an asymptotic Cauchy problem on scri. More specifically, we extract conditions on scri which characterize the vanishing of the MST. Furthermore, we provide a classification of $\Lambda>0$-vacuum space-times with vanishing MST and conformally flat scri which complements the one given by Mars and Senovilla. For this purpose we shall briefly review the asymptotic Cauchy problem in GR and discuss the additional conditions which need to be imposed on the initial data to end up with vacuum space-times with a Killing vector field.

Abstract: In the last 15 years there was spectacular progress in the rigorous analysis of finite-time blowup in nonlinear wave equations. Many of these studies were actually motivated by the desire to obtain a better understanding of singularity formation in Einstein's equations. Mainly based on personal taste, I will discuss some of the most important contributions.

Abstract: The Unruh effect is a fundamental phenomenon of quantum field theories in Riemannian spacetimes. In Minkowski spacetime it expresses the fact that a uniformly accelerated observer perceives the Minkowski vacuum state as a thermal equilibrium state at a certain acceleration-dependent temperature. The physical significance of this observation is still a controversial topic. In this talk an algebraic formulation of the Unruh effect (by G.L. Sewell) is discussed. I provide a brief introduction to the necessary tools from quantum statistical mechanics and local quantum physics. This serves as a preparation for a second talk about a new thermal interpretation of the Unruh effect by D. Buchholz and C. Solveen.

Abstract: Based on the algebraic setting of the Unruh effect discussed in the previous talk ("Algebraic Foundations of the Unruh Effect"), I present recent results by D. Buchholz and C. Solveen on a new interpretation of the thermal aspects of the Unruh effect for scalar free fields. If the notion of temperature is defined using so-called local thermal observables, the local temperature of the Minkowski vacuum is zero also for the accelerated observer. Finally, I mention some open physical questions in this approach.

Abstract: Conformal Yano-Killing (CYK) tensors are natural generalizations of conformal covector fields to the case of higher-rank differential forms. They are often responsible for hidden symmetries. Several spacetimes possess CYK tensors: Minkowski (the components are quadratic polynomials), (anti)de Sitter (a natural construction), Kerr (type-D spacetime), Taub-NUT (they lead to new symmetric conformal Killing tensors). CYK tensors are useful in several situations: Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness which guarantees well-defined total angular momentum; Conserved quantities: asymptotic gravitational charges; Quasi-local mass and "rotational energy" for the Kerr black hole; Symmetries of the Dirac operator; Symmetries of Maxwell equations. These nice geometrical objects are well worth studying in detail.

Abstract: The talk discusses constraints on the global topology of the universe from CMB data, in particular constraints on torus topologies T^3, T^2 x R and S^1 x R^2. The theoretical predictions are compared with experimental CMB data. See also http://particle.univie.ac.at/seminars/particle-physics/

Abstract: Constructing broad classes of (physically relevant) initial data for the Cauchy problem is an important issue in general relativity. From the Gauss and Codazzi equations, the 0th order initial data (the metric induced on a Cauchy surface) and the first order initial data (the second fundamental form of the Cauchy surface) cannot be chosen arbitrarily: they have to satisfy some constraint equations. One of the main methods for studying these equations is the conformal method which was highly successful for constructing and classifying constant mean curvature (CMC) initial data. However, constructing non CMC initial data remains a widely open subject. In this talk I will describe recent results on the construction of solutions to the constraint equations with non constant mean curvature by the conformal method.

Abstract: We give a concise proof of nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability follows by an energy argument. We prove in addition that the development of non-CMC initial data close to the background contains a CMC hypersurface, which in turn implies that stability holds for arbitrary perturbations. This is joint work with Klaus Kroencke (Regensburg).

Abstract: The concept of a closed trapped surface (a spacelike surface with decreasing area in the direction of the future-directed null normals) was introduced by Penrose for the formulation of his first singularity theorem. It is not a priori clear whether such trapped surfaces are evolutionary, and hence an important question is to understand whether/how trapped surfaces can form starting from initial data that do not contain such surfaces. Christodoulou pioneered this work in the vacuum and scalar field case, results for Einstein-Vlasov spacetimes are also known. In my talk I will present first results for Einstein-Euler spacetimes in spherical symmetry, carried out in joint work with Philippe LeFloch (see also arXiv:1411.3008).

Abstract: The understanding of the strong coupling phenomena at qualitative and quantitative level is a challenging task. The best way to attack this problem is at present is the duality between two (or more) theories. The purpose of this lecture is to introduce the basic contemporary concepts of string (gravity)/gauge theory duality and discuss some of their features. The main focus will be on the so-called AdS/CFT correspondence. I'll briefly discuss simple examples of the so-called "brane engineering" of some gauge theories. The "magic" appearance of W-symmetries will be also very briefly discussed.

Abstract: Quantum physics differs from classical physics in that no definite values can be attributed to observables independently of the measurement context. However, the notion of time and of causal order preserves such an objective status in the theory: all events are assumed to be ordered such that every event is either in the future, in the past or space-like separated from any other event. The possible interplay between quantum mechanics and general relativity may, however, require superseding such a paradigm. I will approach this problem in two steps. Firstly, I will consider a single "clock" - a time-evolving (internal) degree of freedom of a particle - to be in a superposition of regions of space-time with different ticking rates. While the "time as shown by the clock" is not well-defined, there is still the notion of global time. Secondly, I will consider that space-time itself is in a superposition, and show that this situation gives rise to quantum correlations for which one cannot say that one event is before or after the other. Finally, I will comment on possible implications of this result for quantum computation.

Abstract: Details on URL http://particle.univie.ac.at/de/seminare

Abstract: The so-called cosmological concordance model of a Cold Dark Matter (CDM) dominated universe predicts a huge number of low-mass CDM subhalos to exist and to surround massive galaxies with an almost isotropic distribution. For our Milky Way and the neighboring Andromeda galaxy these both requirements are significantly contrasted by observations. Not only that the observed number of satellite galaxies is orders of magnitude smaller - the so-called missing-satellite problem - moreover, their spatial distributions are confined to thin planes with coherent orbits.
Nevertheless, unusually high mass-to-light ratios are derived for the dwarf spheroidal galaxies around the Milky Way, lending strong support of their large CDM content. In order to approach consistency of the observational restrictions with the CDM cosmology, over the recent years various scenarios are constructed which will be critically illuminated in this talk with respect to their verification. Conclusively, an alternative solution for the formation of dwarf galaxies in general will be discussed.

Abstract: We turn away from the idea that the Misner spacetime should be Hausdorff as was already discussed by previous authors. In lieu thereof we allow the notion of a non-Hausdorff spacetime and construct an analytic non-Hausdorff extension of Misner space. On this basis we elucidate the global causal structure of the maximally extended Misner spacetime, with the result that there are two fundamentally different maximal extensions and associated covering spaces. From this we can conclude that there exist two versions of Misner space. Furthermore, we wish to shed some new light on the pathologies, e.g. the quasiregular singularities and CTCs. It turns out that the Misner space is related to the pseudo-Schwarzschild spacetime regarding its properties from a chronological and global point of view. According to this result the pseudo-Schwarzschild cylinder can be regarded as a non-flat generalization of the Misner space. This gives rise to a conjecture which says that 4D Misner space and pseudo-Schwarzschild spacetime are isocausal to each other. Furthermore, we create a new chronology violating spacetime that describes a generalization of the two precedent ones: We derive the pseudo-Reissner-Nordstroem spacetime from the well-known Reissner-Nordstreom spacetime and review our main results in this more general setting.

Abstract: We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius α. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter α. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.

Abstract: We introduce a class of overdetermined systems of partial differential equations of on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise to various important classes of equations in differential geometry.
Among them there are: the Ricci soliton equations, the vacuum near-horizon geometry equations in general relativity, special cases of Einstein-Weyl equations and their projective counterparts, equations for homotheties and Killing's equation. We provide explicit examples of generalised Ricci solitons in 2 dimensions, some of them obtained using techniques developed by J.Jezierski. This is joint work with Pawel Nurowski available at arXiv:1409.4179.

Note the 10th Vienna Central European Seminar on Particle Physics and Quantum Field Theory - Inflation and Cosmology, Friday November 28 to Saturday November 29, 2014

Abstract: We report on recent progress in the study of spacetimes where the metric is C^{0,1} (locally Lipschitz continuous) or C^{1,1} (first derivatives locally Lipschitz). In particular, we focuss on existence and regularity of geodesics in the first case and discuss the prospects of proving Hawking's singularity theorem in the second case.

Abstract: We explain how fuzzy geometries in extra dimensions can emerge in standard Yang-Mills gauge theory, based on a geometric version of the Higgs effect. In particular, we discuss the 4-and 6-dimensional squashed coadjoint orbits which were recently found in maximally supersymmetric N=4 SYM. The resulting low-energy fluctuation modes lead to 3 generations of chiral fermions coupled to scalar and gauge fields. The discussion is focused on geometrical and group-theoretical aspects. Talk based on arXiv:1409.1440

Abstract: I will introduce the basic concepts of String theory and show how the quantized string unifies gauge theory and gravity. I will further explain why String Theory requires a ten-dimensional space-time and discuss the concept of compactification of extra dimensions.

Abstract: I discuss the recent claim of experimental verification of an analogue of the Hawking effect.

Abstract: Interaction between the components in galaxy clusters - the galaxies and the gas surrounding the galaxies, the so-called intra-cluster medium - have a variety of effects on the cluster. The gas within the galaxies is compressed and sometimes stripped off. Therefore the galaxies change their morphology and their star formation activity. The intra-cluster gas is enriched by the lost gas from the galaxies, hence it changes the metal content and the temperature. All effects are modelled by simulations on galaxy scales as well as clusters scales. Results of the evolution of various properties (metallicity, gas density, star formation rate, temperature, magnetic fields,... ) are presented.

Abstract: Conformal compactification is a well established tool in GR and many related fields. The model for this construction is often taken to be the Poincare ball model of hyperbolic space. There is a refinement of this idea which reveals the Lie groups and Lie group embeddings behind conformal compactification. These structures at once generalise to the curved setting through the conformal Cartan-tractor calculus (i.e. the natural conformally invariant connection and related objects). This provides a conceptual and calculationally effective way to treat many problems linked to conformal compactification.

Abstract: A method for analysing the evolution of the volume of an inhomogeneous irrotational dust universe is presented. In this framework it is possible to go beyond perturbation theory in a numerical analysis. The results of such computations show that the evolution is strongly affected by inhomogeneities, but nevertheless suggest that a cosmological constant is required to account for the observed acceleration of the expansion. Possible loopholes to this conclusion will be discussed.

Abstract: We construct a class of vacuum space-times without Killing vectors and with "asymptotically velocity dominated" singularities.

Abstract: In 2008 Sergio Dain proved that the ADM mass of axially symmetric, AF initial data is greater or equal than the root of the angular momentum, and equality holds for extreme Kerr (only). We describe recent, stronger inequalities which also contain higher "momenta", focusing on the special case where the data are close to extreme Kerr in a suitable sense.

Abstract: I will describe bifurcation phenomena in thevacuum Lichnerowicz equation with positive cosmological constant on $S^1\times S^2$ with $U(1)\times SO(3)$-invariant seed data.

Abstract: I describe the construction of certain classes of axially symmetric initial data with positive cosmological constant via the conformal method.

Abstract: I will explain how the well-known vector field method, which was one of the most important tool to understand the asymptotic behavior of the wave equation, can also be applied to the Vlasov fields.

Abstract: I will describe ongoing work on the construction of solutions to the collisionless Boltzmann equation on a Kerr black hole background.

Abstract: I will briefly describe my research project on acoustic perturbations of radial accretion flows.

Abstract: We continue our discussion of the geometry and topology of asymptotically flat initial data sets, including discussion of a different approach based on solutions of Jang’s equation.

Abstract: With a distance of about 8 kpc, the center of the Milky Way is the closest galactic nucleus to us. Hence, it provides us with a unique opportunity to study a galactic nucleus up close. Longterm observations of stellar kinematics of the Nuclear Star Cluster point to the existence of a super-massive black hole (SMBH) at the position of Sagittarius A* (SgrA*), with a mass of 4 million suns. SgrA* shows flare emission from the millimeter to the X-ray domain. A detailed analysis of the infrared light curves allows us to address the accretion phenomenon in a statistical way. The analysis shows that the near-infrared flare amplitudes are dominated by a single state power law, with the low states in SgrA* limited by confusion through the unresolved stellar background. There are several dusty objects in the immediate vicinity of SgrA*. The source G2/DSO is one of them. Its nature is unclear. It may be comparable to similar stellar dusty sources in the region or may consist predominantly of gas and dust. In this case a particularly enhanced accretion activity onto SgrA* may be expected in the near future.

A relativistic model that could explain the flaring nature of SgrA* are hotspots, overdense compact emitting regions, moving inside an accretion flow. To model compact sources orbiting in the immediate vicinity of SgrA*, it is necessary to use the metric for a rotating black hole, the Kerr-metric. There are a couple of relativistic effects on the emission that need to be taken into account, most importantly the gravitational Doppler-shift and gravitational lensing.

Abstract: We consider the static Einstein-Vlasov system in spherical symmetry. Existence of different types of solutions to this system for zero cosmological constant has been shown for the isotropic and anisotropic case by Rein-Rendall, Rein and Wolansky. In this talk I review the results on static solutions for the Einstein-Vlasov system and eventually describe a method to prove existence of static solutions to the Einstein-Vlasov system with positive cosmological constant. The energy density and the pressure of these solutions have compact support and outside a finite ball these solutions are identical to a Schwarzschild deSitter spacetime. The results presented in the talk are joint work with H. Andréasson and D. Fajman.

Abstract: The dynamical gravitational collapse of a complex scalar field coupled with Maxwell field in dilaton gravity, allowing a phantom coupling to gravity, will be described.

Abstract: Known theorems and work in progress establishing the existence of solutions describing isolated bodies will be discussed. There are results for fluids as well as for elastic matter, with and without gravity in Newtonian and Einstein's theory.

Abstract:We give an elementary proof of positivity of the Trautman-Bondi mass of light-cones with complete generators in asymptotically flat space-times.

Abstract: We present a geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center of mass of geometrostatic systems (Huisken-Yau, Metzger, Huang). We then explain the pseudo-Newtonian character of these formulas and show that they converge to Newtonian mass and center of mass in the Newtonian limit, respectively, using Ehlers' frame theory. Moreover, we present a novel physical interpretation of the level sets of the canonical lapse function and apply it to prove uniqueness results.

Abstract: We discuss the initial-boundary value problem which arises when formulating the Cauchy problem in general relativity on a finite domain with an artificial outer boundary, like is usually the case in numerical relativity simulations. First, the restrictions on the boundary data that result from the requirement of constraint propagation and the attenuation of spurious reflections will be analyzed. Then, we will introduce the important concept of strong well-posedness and explain it first in the simple example of the wave equation on the half-plane. For systems of wave equations, strong well-posedness allows to treat a certain class of boundary conditions which is general enough to cover many evolution systems in physics, including Einstein’s equations in harmonic coordinates. Finally, open issues related to a geometric formulation of the initial-boundary value problem will be mentioned.

Abstract: Recent results concerning derivation of the conservative equations of motion of compact binary systems up to the 4th post-Newtonian approximation of general relativity will be presented. The derivation is made within the ADM canonical formalism. It employs Dirac delta distributions to model the compact bodies what leads to divergencies which are regularized by a combination of Riesz-implemented Hadamard's partie finie approach and dimensional regularization. It also requires taking into account tail-transported nonlocal-in-time interaction between the bodies.

Abstract: I will discuss an ongoing project on flat steady states for the Vlasov-Poisson system, which in astrophysics are used as models of disk-like galaxies. We construct solutions numerically and study in particular the shape of the rotation curves. It is often claimed that a system obeying Newton's law of gravity should have a rotation curve which declines in a Keplerian manner far out in the galaxy. However, observations indicate that the rotation curves are approximately flat and this discrepancy is one of the reasons for introducing dark matter. In our numerical study we find a large class of solutions for which the rotation curves are flat all the way out to the boundary of the steady state. This is a joint work with Gerhard Rein.

Abstract: We discuss some results concerning the geometry and topology of asymptotically flat initial data sets in three and higher dimensions, with and without horizons. More specifically, we explore the relationship between the topology of such initial data sets and the occurrence of marginally outer trapped surfaces in the initial data. We shall discuss the rationale for this and present relevant background material. This involves work with several collaborators, L. Andersson, K. Baker, M. Dahl, M. Eichmair and D. Pollack.

Abstract: I will give an introduction to the linearization stability problem for the Einstein equations. Furthermore I will introduce two criterions for linearization stability (established by Vincent Moncrief [1][2]) and sketch the corresponding proofs from those references.
[1] V. Moncrief, Spacetime symmetries and linearization stability of the Einstein equations. I ,
J. Math. Phys. 16, 493 (1975); dx.doi.org/10.1063/1.522572
[2] V. Moncrief, Spacetime symmetries and linearization stability of the Einstein equations. II ,
J. Math. Phys. 17, 1893 (1976); dx.doi.org/10.1063/1.522814

Abstract: I will describe a configuration space of two surfaces rolling on each other without sleeping or twisting. A relation between this space and totally null planes in 4-dimensional conformal geometry of signature (2,2) will be established and used to construct new surfaces that roll on each other without sleeping or twisting and exhibit the symmetry of the exceptional simple Lie group G2.

Abstract: Some results on the mechanism of interactions among fermion fields and cosmic strings in curved spacetime, as well as on the influence of spinor fields on Yang-Mills black holes, will be presented.

Abstract:
1. A short introduction to convenient calculus in infinite dimensions.
2. Manifolds of mappings (with compact source) and diffeomorphism groups as convenient manifolds
3. A diagram of actions of diffeomorphism groups
4. Riemannian geometries of spaces of immersions, diffeomorphism groups, and shape spaces, their geodesic equations with well posedness results and vanishing geodesic distance.
5. Riemannian geometries on spaces of Riemannian metrics and pulling them back to diffeomorphism groups.
6. Robust Infinite Dimensional Riemannian manifolds, and Riemannian homogeneous spaces of diffeomorphism groups.
We will discuss geodesic equations of many different metrics on these spaces and make contact to many well known equations (Cammassa-Holm, KdV, Hunter-Saxton, Euler for ideal fluids), if time permits. 

Abstract: I will review the status of a conformal constrained ADM-like formulation of the Einstein (+matter) equations on hypersurfaces of constant mean curvature, developed with V. Moncrief. This has been adapted and implemented numerically for several applications: a gravitationally perturbed Schwarzschild black hole in axisymmetry, late-time tails of massless scalar and Yang-Mills fields in spherical symmetry, critical phenomena in the Einstein-Yang-Mills system, and massive scalar fields / evolution of (mini) boson stars.

Abstract: Newton’s Law of Gravity is considered valid from sub-millimetre distances up to inter-galactic space, but fails to describe important features of cosmology like the accelerating expansion component of our universe. While the most straightforward candidate for such a component is Einstein’s cosmological constant, a plausible alternative is dynamical vacuum energy, or ”quintessence”, changing over time. Although it is traditional to neglect (or set to zero) the couplings of this light scalar to the standard model, it is natural for a scalar quintessence field to evolve on cosmological time scales today while having couplings to matter, as expected from string theory. Hence the presence of such a field would provide energy changes to Newton’s gravity potential of the earth at short distances invisible to electromagnetic interactions.

We present a novel direct search strategy with neutrons based on Rabi spectroscopy of quantum transitions in the gravity potential of the earth. The sensitivity for deviations on Newton’s gravity law is right now E = 10^-15 eV, providing a severe restriction on quintessence fields and on any possible new interactions on that level of accuracy. If some undiscovered dark matter or dark energy particles interact with a neutron, this should result in a measurable energy shift of the observed quantum states. In the case of some dark energy scenarios with a coupling to matter, the experiment has the potential to find or exclude these hypothetical particles in full parameter space.

Abstract: I discuss the recently announced discovery of a B-mode signal in the cosmic microwave background and its significance for cosmology.

Abstract: In this talk I will make use of a representation of the Einstein Cosmos based on the properties of conformal geodesics to discuss the global evolution in time of massless spin-2 fields. In view of the conformal properties of the massless spin-2 equation, the constructed solutions can be reinterpreted as global solutions in the anti de Sitter space-time. I will discuss how this analysis can be generalized to the case of the conformal field equations.

Abstract. Joint Work with Philippe G. LeFloch. We consider vacuum spacetimes with two spatial Killing vectors and with initial data prescribed on T^3. The main results that we will present concern the future asymptotic behaviour of the so-called polarized solutions. Under a smallness assumption, we derive a full set of asymptotics for these solutions. Within this symetry class, the Einstein equations reduce to a system of wave equations coupled to a system of ordinary differential equations. The main difficulty, not present in previous study of similar systems, is that, even in the limit of large times, the two systems do not directly decouple. We overcome this problem by the introduction of a new system of ordinary differential equations, whose unknown are renormalized variables with renormalization depending on the solution of the non-linear wave equations.

Abstract: We exhibit a class of theories, with the relativistic fluid a special case, which naturally take the form of a symmetric hyperbolic system. The 'reason' for this is that they possess a convex extension, with the role of convex entropy being played by the particle number density. This is joint work with Philippe LeFloch.

Abstract: In this talk, I discuss a peculiar black hole instability that arises in the presence of short distance dispersion. Its origin is to be found in the spectral properties of the wave equation on a background geometry containing two horizons. I will start by qualitatively describing this effect. In a second part, I will show that the presence of complex eigen-frequencies in the spectrum encodes this instability. Such eigen-frequencies are allowed only because the conserved scalar product is non positive definite. I will then compute the spectrum through a WKB approximation. In a last part, I will present an abstract toy model to discuss general feature of the appearance complex eigen-frequencies. This model is directly inspired from the ``Friedrich model'' of resonances. This will allow to make contact with quasi-normal modes of black holes and other known black hole instabilities.

Abstract: I will describe results of my joint work with Piotr Bizoń on instability of three-dimensional asymptotically AdS spacetime coupled to a massless scalar field. As in higher dimensions, for a large class of perturbations we observe a turbulent cascade of energy to high frequencies, However, in contrast to higher dimensions, small perturbations cannot evolve into a black hole, because their energy is below the threshold for a black hole formation. To determine the long-time evolution we use the analyticity strip method, well known in fluid dynamics, which provides a powerful numerical tool.

Abstract: We review recent and older work on impulsive gravitational waves. These space-times have become textbook examples modelling short but intense gravitational wave impulses. Mathematically they have been described by a distributional - the so-called Brinkmann - metric as well as by a continuous metric - referred to as Rosen form. Our main focus will be on geodesics in these geometries. First we will discuss the behaviour and regularity of geodesics in the distributional form and the notion of geodesic completeness in an even wider class of impulsive wave-type spacetimes. Then we will turn to the Rosen form, and examine the regularity of geodesics in the various subclasses of impulsive wave spacetimes.

Abstract: This talk will explore issues related to the motion of extended bodies in curved spacetimes. Non-perturbative notions of linear and angular momentum will be introduced and some of their properties discussed. Most important among these properties is that forces and torques are “almost” preserved by a certain class of deformations which may be applied to the relevant field (electromagnetic, gravitational, or otherwise). Here, the “almost” refers to terms which can be interpreted purely as finite shifts in an object’s apparent multipole moments. The freedom to choose different fields can be used to dramatically simplify problems where self-interaction affects the motion. Usual results on the self-force emerge as a simple special case of this formalism. In another special case, full multipole expansions for the forces and torques acting on extended test bodies are recovered as well.

Abstract: The behaviour of particles, both from a classical as well as a quantum mechanical perspective, with respect to impulsive background fields is investigated. Due to the singular nature of the problem, which requires the definition of products of distributional objects, a generalized framework like Colombeau's new generalized functions has to be used.

Abstract: The study of the asymptotic behavior of the Maxwell and gravitational fields is a key point in the understanding of the stability properties of solutions of the Einstein equations. Penrose introduced in the beginning of the 60s a method based on the construction of Hertz potentials satisfying a wave equation to determine the asymptotic behavior of massless free fields of arbitrary spin from a decay Ansatz on solutions of the scalar wave equation. The purpose of this talk is to adapt this idea in the context of a Cauchy problem: consider a Cauchy problem for the Maxwell and gravitational fields on the Minkowski space-time with initial data in weighted Sobolev spaces;  in the framework of this Cauchy problem, the existence of a Hertz potential is proved; finally, from a standard decay result for the scalar wave equation, the asymptotic behavior of these higher spin fields is derived. The classical decay results for Maxwell and gravitational fields are recovered.

Abstract: Wave maps are maps from a Lorentzian manifold to a Riemannian manifold which are critical points of a Lagrangian which is a natural geometrical generalization of the free wave Lagrangian. Self-gravitating wave maps are those from an asymptotically flat Lorentzian manifold which evolves according to Einstein's equations of general relativity with the wave map itself as the source. The energy of wave maps is scale invariant if the domain manifold is 2+1 dimensional, hence it is referred to as the critical dimension.

Apart from a purely mathematical interest, the motivation to study critical self-gravitating wave maps is that they occur naturally in 3+1 Einstein's equations of general relativity. Therefore, studying critical self-gravitating wave maps could be a fruitful way of understanding the ever elusive global behavior of Einstein's equations. A few central questions concerning the study of critical self-gravitating wave maps are local and global existence, blow up profile, compactness and bubbling.

In this talk, after a brief discussion on the background and formulation of the Cauchy problem of critical self-gravitating wave maps, we shall present a recent proof of the non-concentration of energy of critical equivariant self-gravitating wave maps before pointing out potential generalizations and applicable methods therein.

Abstract: I give an introduction to quantum field theory on curved spacetimes in the framework of locally covariant field theories,   introduced by Brunetti, Fredenhagen, Verch and Hollands, Wald. The main motivation and example will be the covariant definition of the stress-energy tensor of a scalar quantum field.

Abstract: The present work concerns the construction of a lightlike foliation of spacetime which suites the Kerr-Schild framework describing the gravitational field of a massless particle located on the horizon. Despite of being defined only on local grounds, the gained results do not only prove to be consistent to former works of Hayward and Brady, Israel, Droz and Morsink, but fit also former results of Moncrief and Isenberg and, in addition, that of Friedrich, Racz and Wald concerning Gaussian null coordinates. Two simple examples for the construction, describing the situation for a Schwarzschild black hole in Kruskal-Szekeres as well as in Kerr-Schild coordinates, are given. Finally it is explained how the obtained foliation might be used in order to extend the gravitational field of a massless particle off the horizon.

Abstract: I review the basic setup of Kaluza-Klein theory, namely a 5-dim. vacuum with a cyclic isometry (a U(1) fibre bundle over 4-dim. spacetime) which corresponds to Einstein-Maxwell-dilaton theory. I show that the property of compact surfaces of being (stably) marginally trapped is preserved under lift and projection provided the appropriate ("Pauli-") conformal scaling is used for the spacetime metric. I also discuss recently proven area inequalities for stable axially symmetric 2-dimensional and 3-dimensional marginally outer trapped surfaces. This talk is based on joint work with Tim-Torben Paetz, arxiv.org/abs/1302.3052

Abstract: More than 95% of the matter in the Universe is invisible. An overview of our current understanding of abundance and properties of dark energy and dark matter is presented. The first part focusses on issues pertaining to dark matter including observational evidence for its existence and current constraints. MOND is briefly mentioned. The second part focusses on dark energy. Observational strategies to detect and quantify dark energy are reviewed. In particular, recent results from the Planck mission are presented and an overview of the new ESA dark energy mission Euclid is given.

Abstract: I describe ongoing joint work with D. Fajman on this topic. Our inspiration comes from the work arxiv.org/abs/1109.5602 on the pure Einstein-Maxwell case, and from the known strange exact solutions in Einstein-Maxwell-dilaton theory.

Abstract: Newton's Inverse Square Law has been examined in detail from the sub-millimetre scale up to inter-galactic distances. His gravity prediction for these systems is considered valid, but fails to describe important features of cosmology like the accelerating expansion of our universe. While the most straightforward candidate is Einstein's cosmological constant , a plausible alternative is dynamical vacuum energy, or "quintessence", changing over time. Although it is traditional to neglect the couplings of this light scalar to the standard model, some scenarios allow scalar quintessence field to evolve on cosmological time scales today while having couplings to matter, as expected from string theory . Hence the presence of such a field would provide energy changes to Newton's gravity potential of the earth at short distances invisible to electromagnetic interactions. We present a novel direct search strategy with neutrons based on Rabi-spectroscopy of quantum transitions |1> ↔|2>, |1> ↔|3>, |2> ↔ |4>, |2> ↔|3>, and |2> ↔ |4>$ in the gravity potential of the earth. The sensitivity for deviations on Newton's gravity law is right now E = 10-14 eV, providing a severe restriction on quintessence fields and on any possible new interactions on that level of accuracy.

Abstract: I will give an exhaustive description of Killing Initial Data on light-cones, and on transversally intersecting characteristic hypersurfaces, in vacuum space-times.

Abstract: The talk first resumes some recent progress towards the goal to find time functions for a given globally hyperbolic metric for which basic geometric quantities are bounded. Then we conversely fix a time function and ask whether there is a conformal factor such that the corresponding Cauchy surfaces are of bounded geometry which provides us with Sobolev embeddings and denseness results for spaces of initial values. This is done by using a recently developed method called flatzooming which has proven to be powerful in different contexts of Riemannian and Lorentzian geometry.

Abstract: Via the geodesics of the Levi-Civita connection, a pseudo-Riemannian metric on a smooth manifold M determins a projective structure on M. Similarly to the role of the conformal geometry, this projective structure can be used to identify particularly robust properties of pseudo-Riemannian manifolds. Reporting on joint work with A.R. Gover (Auckland) my talk will be devoted to the projective analog of the notion of a conformally compact Riemannian metric. This exhibits a notion of compactification for Ricci flat metrics and non-Ricci-flat Einstein metrics which are similar to - but different from - the ususal notion of conformal compactifications.

Abstract: Geometric inequalities have been of interest in General Relativity in recent years. From them, it is possible to relate physical quantities that have a precise geometric meaning--like mass, area, charge and angular momentum--, and thus be able to predict significant consequences on the evolution and stability of some physical systems. In this talk, I present a conjecture relating the electrical charge to the size of a real object, inspired on the hoop conjecture valid for black holes. First I discuss briefly some relevant aspects of the hoop conjecture and then I state the analogous conjecture for real objects in general. Physical motivation of the inequality is discussed, as well as define with precision what we understand about the "size” of a three dimensional object. As a first approach, I study the spherical problem with ECD wherein this conjecture is precisely formulated and I show that it is true outside and in the bound of the sphere.

Abstract: Light bending, characteristic of geometric descriptions of gravity as spacetime curvature, manisfests dramatically in the existence of black hole spacetimes. Global notions associated with the causal disconnection between spacetime regions, on the one hand, and (quasi-)local concepts related to the convergence of light rays, on the other hand, provide complementary tools for the study of black holes. Here we focus on the latter aspects, namely relying on the notion of trapped surface. More specifically, we discuss the role of the limiting case provided by marginally (outer) trapped surfaces (MOTS) as probes into the geometry of dynamical black holes, placing a special emphasis in their notion of stability. We illustrate the discussion with two examples, the first one dealing with a family of geometric inequalities providing a lower bound for the horizon area, and the second one motivating the role of MOTS as inner "test screens" in a heuristic proposal for a "scattering-like approach" to the a posteriori analysis of dynamical black hole spacetimes.

Abstract: In my talk I will discuss two possible nontrivial scenarios concerning the fate of Lorentz symmetry in the low energy limit of quantum gravity: Lorentz Invariance Violation (LIV) and Lorentz/Poincare symmetry deformation. I will also briefly present some of the experimental bounds on the parameters of the models pertaining to these scenarios

Abstract: There is a strong evidence that anti-de Sitter space is unstable due to small generic perturbations. It is also believed that there might exist solutions that do not lead to the formation of a black hole. I will discuss recent analytical and numerical results concerning time-periodic solutions for Einstein-massless-scalar field system with negative cosmological constant, in particular how to construct such stable configurations. If time permits I will outline the pure vacuum case. The talk will be an extension of joint work with Andrzej Rostworowski presented in the paper arxiv:1303.3186.

Abstract: I will present an alternative to the Dirac quantization of minisuperspaces that admits a time evolution.

Abstract: Summarising my diploma thesis I will start with introducing the work of Hubert Bray being the paper my thesis is built up upon. The paper deals with a possible explanation of the existence of dark matter by introducing a torsion of space-time. Its basic idea is to derive an extension of General Relativity involving a more general connection from particular axioms for the metric and the connection. According to these axioms the gravitational action functional can only take a specific form. The variation of this action functional leads to Einstein-Klein- Gordon equations. The mass term in the Klein-Gordon equation corresponds to the coupling constant for the torsion. The terms involving the scalar field and its gradient appearing in the Einstein field equations can be interpreted as the effective energy-stress tensor and can be attributed to dark matter. The solution of the Klein-Gordon equation in a spherically symmetric space-time is an oscillating function both in time and space. From the effective energy-stress tensor appearing in the Einstein field equations we derive a Newtonian potential displaying a slowly rotating maximum, which resembles a spoke. In the paper the author performs simulations using this Newtonian potential and obtains results resembling a spiral galaxy. The aim of my diploma thesis is to investigate the measurable effects of the torsion field by analysing the behaviour of a particle with spin-1/2 in the torsion field. The polarization vector of a particle in a torsion field is subject to a torque and hence precesses. To compute the precession two different approaches were chosen: the first one is the supersymmetric approach that enables one to consistently couple a classical spinning particle to the torsion field. The second approach is a quantum mechanical one solving the Dirac equation minimally coupled to the torsion field. The conclusion of my thesis is that the precession of the polarization vector induced by the torsion field results in an oscillatory motion with the deflection of order of magnitude 10^-6 rad. The sense of rotation of the precession changes every half period of the time oscillation of the torsion field.

Abstract: A broad class of theories based on non-linear Lagrangians will be discusssed and their equivalence/nonequivalence with Einstein theory (possibly with additional matter fields) will be analyzed. To simplify technical aspects of such theories, a nonstandard theory of curvature will be used.

Abstract: Following the parts of my thesis, I will first give a brief introduction to the field of spatially homogenous (SH) cosmology with an emphasis on the use of dynamical systems methods to analyse the evolution of these cosmologies qualitatively. After this, I will summarise the results of the central part of my thesis, which deals with the dynamical system analysis of a special class of SH cosmologies (locally rotationally symmetric Bianchi type VIII). The matter content is thereby chosen out of a very general family which allows for anisotropic pressures, and contains physically relevant models like perfect fluids, elastic matter or collisionless matter. The goal was to investigate how the grade of anisotropy of the matter influences the qualitative dynamics, which was achieved via a comparison with the well known results with perfect fluids. It is shown that there are indeed cases where the qualitative dynamics can differ significantly in both, the past and future asymptotics. If time is left I would like to close my talk with a little eye candy, by presenting a Maple document, which allows to plot the solutions to each matter configuration as a flow diagram by a single click on the matter-parameter space.

Abstract: We shall discuss conformally flat hypersurfaces in the realm of Moebius geometry. Particular attention will be paid to the transformation theory and integrable nature of this class of hypersurfaces.

Abstract: I will present a Hamiltonian approach to the definition of mass for a class of asymptotically cylindrical initial data sets. This is based on joint work in progress with Jezierski and Kijowski.

Abstract: We will consider a configuration space of two solids rolling on each other without slipping or twisting, and will identify it with an open subset U of R⁵. It turns out that U is naturally equipped with a generic distribution D of 2-planes. We will discuss symmetry properties of the pair (U,D) and will mention that, in the case of the two solids being balls, when changing the ratio of their radii the dimension of the group of local symmetries unexpectedly jumps from 6 to 14 . This occurs for only one such ratio, and in such case the local group of symmetries of the pair (U,D) is maximal. It is maximal not only among the balls with various radii, but more generally among all (U,D)s corresponding to configuration spaces of two solids rolling on each other without slipping or twisting. This maximal group is isomorphic to the split real form of the exceptional Lie group G2. In the remaining part of the talk we will argue how to identify the space U defined above with the bundle T of totally null real 2-planes over a 4-manifold equipped with a split signature metric. We call T the twistor bundle for rolling bodies. We show that the rolling distribution D, can be naturally identified with an apropriately defined twistor distribution on T. We use this formulation of the rolling system to find more surfaces which, when rigidly rolling on each other without slipping or twisting, have the local group of symmetries isomorphic to the exceptional group G2

Abstract: Quantum optics provides a high-precision toolbox to enter and to control the quantum regime of the motion of massive mechanical objects. This opens the door to a hitherto untested parameter regime of macroscopic quantum physics. Due to the large available mass range - from picograms in nanomechanical waveguides to kilograms in mirrors for gravitational wave detection - it becomes possible to explore the fascinating interface between quantum physics and (quantum) gravity in table-top quantum optics experiments. I will discuss a few examples.

Abstract: The perturbations of black hole spacetimes, when decaying, show characteristic (damped) oscillations called quasi-normal modes. The asymptotically highly damped modes are widely suspected to carry information about certain black hole quantum properties in the semi-classical limit. We analyse the behavior of asymptotic quasi-normal frequencies of static black hole spacetimes and interpret the meaning of the results, linking them to possible quantum properties of spacetime. We analyse our suggestions in the broader context of spacetime thermodynamics and discuss some open questions.

Abstract: I will discuss some conformal properties of the extremal Reissner-Nordström spacetime ---in particular in what concerns the behaviour of the spacetime close timelike infinity. I will show how Friedrich's construction of the "cylinder at spatial infinity" can be used, together with a conformal discrete symmetry of the spacetime, to show that there exists a conformal representation of timelike infinity in this spacetime for which the various conformal field quantities and equations regular. I will also discuss some numerical evidence of this conformal representation.

Abstract: A compact Einstein metric is called Linearly stable if the second variation of the Einstein-Hilbert functional is nonpositive on TT-tensors.
We will discuss curvature conditions which ensure stability. Then we will show that under certain conditions on the spectrum of the Laplacian, linear stability implies that the given Einstein manifold is an attractor of the Ricci flow.

Abstract: An introduction is given to some recent developments in Yang-Mills matrix models, focusing on the effective geometry of brane solutions and their possible relevance to gravity in a brane-world picture.

Abstract: Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points couple the equation for harmonic maps with spinor fields. At present, a general existence result for Dirac-harmonic maps is not available.

In the first part of the talk we will introduce the notion of Dirac-harmonic maps and explain their basic properties. We will also summarize what is currently known about the existence of Dirac-harmonic maps. In the second part of the talk we present an approach to the existence question by the so-called heat flow method and explain how far this idea can be pushed.

Abstract: I provide an introduction to 3-dimensional higher spin gravity, review some of the recent developments with particular emphasis on holography and point out some of the puzzling open questions, especially those concerning a geometric interpretation of the field configurations.

Abstract: I consider a spherically symmetric SU(2) Yang-Mills field on the exterior of extreme Reissner-Nordstrom black hole. The problem is equivalent to a Yang-Mills field propagating on a regular asymptotically flat spacetime. Infinitely many non-trivial static solutions are shown to exist. I analyze linear perturbations of the solutions and find their spectrum (unstable modes and quasinormal modes). Then I show the dynamics of the field and the approach to a static solution.

Abstract: Oliver Rinne (AEI) and I developed, a few years ago, a fully constrained method for integrating the vacuum Einstein field equations out to Scri. Oliver subsequently implemented this proposal numerically for the case of axially symmetric metrics and showed that it gave stable evolutions, reproducing in particular (in a fully nonlinear code) the well-known quasi-normal ringing modes characteristic of black holes. In this talk I will describe some very recent work with Oliver in which we have extended the theoretical developments to include conformally invariant matter sources, including Yang-Mills fields and implemented these numerically in the case of spherical symmetry. The extra resolution available in this case permits us not only to recover the ringing but also the (Price law) tails in the various radiation fields.

Abstract: We study the scalar wave equation on the open exterior region of an extreme  Reissner-Nordstr\"om black hole and prove that, given compactly supported  data on a Cauchy surface orthogonal to the timelike Killing vector field, the solution, together with its $(t,s,\theta,\phi)$ derivatives of arbitrary order, $s$ a tortoise radial coordinate, is bounded by a constant that depends only on the initial data. Our technique does not allow to study transverse derivatives at the horizon, which is outside the coordinate patch that we use.  However, using previous results that show that second and higher transverse derivatives at the horizon of a generic solution grow unbounded along horizon generators, we show that any such a divergence, if  present, would be milder for solutions with compact initial data.
This talk is based on lanl.arxiv.org/abs/1209.0213, and it is joint work with G. Dotti.

Abstract: In many cases the mathematical structures which we use in applications (computer science, dynamical systems, general relativity) present both a topology and an order. There is a beautiful but little known topological theory which unifies these concepts into that of 'quasi-uniformity'. In practice one has simply to drop an axiom in topology to find that an order naturally arises. Most of topology can be still developed, leading to concepts such as normally preordered spaces or completely regularly preordered spaces. I wish to introduce and comment on this generalization of topology which allows us to prove, among the other results, the existence of time functions in stably causal spacetimes.

Abstract: In recent years there were renewed interest in extending the black hole uniqueness theorems to space-times which are neither real-analytic nor axially-symmetric. Thus far the results obtained have either been conditional on an additional rigidity assumption of the black hole event horizon, or on an additional smallness assumption of the space-time being suitably "close" to being Kerr(-Newman). I will describe a result of the latter class: that a weighted point-wise control of local space-time geometry yields topological constraints on the domain of outer communications. This provides a rigorous formulation for the intuitively obvious fact that "if on every patch the space-time looks similar to a Kerr-Newman solution, it cannot contain more than one black hole".

Abstract: Solutions to the Einstein-Vlasov system describe spacetimes with collisionless matter. The nonlinear stability problem for the Einstein-Vlasov system with symmetries has been considered in a series of works starting with Rein and Rendall in 1992. Recently, the first result for the Einstein-Vlasov system without symmetry assumptions has been established by Ringström, considering a positive cosmological constant. In the talk, we present the proof of future nonlinear stability of the Einstein-Vlasov system in 2+1 dimensions without symmetry assumptions and no cosmological constant. Due to the slow expansion and low spatial dimension in that situation, it is essential to prove strong decay properties of the energy momentum tensor. We obtain these decay rates, by introducing geometric Vlasov energies using a specific metric on the tangent bundle of spacelike hypersurfaces - the Sasaki metric. We present energy estimates for those energies and their application in the proof of nonlinear stability. Finally, we give an outlook to applications and related work in progress on the corresponding higher dimensional problem.

Abstract: In the first part of the talk a Schwarzschild black hole is considered. We assume that light sources are distributed on a (big) sphere of radius R that emit, at an instant of time, photons isotropically. We calculate the resulting photon distribution and find that in the long-time limit the density becomes infinitely large near the photon sphere at r=3m. This suggests that every Schwarzschild black hole in  nature should be surrounded by a shell of very high photon density which could be detrimental to the health of any observer who comes close to this region. In the second part we discuss how the situation changes if a Kerr black hole is considered.

The first part is based on the Bachelor Thesis of Dennis Philipp and the second part is ongoing work with Arne Grenzebach.

Abstract: We investigate accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation -- its rotational frequency is larger than that given by the well known strictly Keplerian formula that takes into account the central mass only. Thus determination of central mass in systems with massive disks requires great care -- the strictly Keplerian formula yields only an upper bound. The effect of self-gravity depends on geometric aspects of disk configurations. Disk systems with a small (circa 10^{-4}) ratio of the innermost radius to the outermost disk radius have the central mass close to the upper limit, but if this ratio is of the order of unity then the central mass can be smaller by many orders of magnitude from this bound.

Abstract: I discuss the classical motion of electromagnetically bound systems in an external gravitational field and associated quantum effects.

Abstract: The causal ladder of spacetimes is introduced and the role of stable causality is commented. Some details are given of the recent solution to the problem of the equivalence between stable causality and K-causality. In particular this result is used to show that under reasonable conditions the absence of a cosmological time implies the null geodesic singularity of spacetime.

Abstract: I will present a class of diagrams, that we call projection diagrams, as a tool to visualise the global structure of space-times, and show how they can be used for the Kerr-Carter family of metrics with cosmological constant. A seemingly new class of overspinning such solutions with negative cosmological constant and unusual global properties will be presented.

Abstract: I will discuss old and new well posed sets of conformally covariant versions of the vacuum Einstein equations.

Abstract: About twenty years ago, Choptuik studied numerically the gravitational collapse (Einstein field equations) of a massless scalar field in spherical symmetry, and found strong evidence for a universal, self-similar solution at the threshold of black hole formation. We give a rigorous, computer assisted proof of the existence of Choptuik's spacetime, and show that it is real analytic.

This is joint work with E. Trubowitz.

Abstract: In this talk I am going to present the results of a recent paper [2], in which we show that the regularity of the gravitational metric tensor cannot be lifted from C^0,1 to C^1,1 by any C^1,1 coordinate transformation in a neighborhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel’s celebrated 1966 Theorem, which states that such coordinate trans-formations always exist in a neighborhood of a point on a smooth single shock surface [1]. The results imply that points of shock wave interaction represent a new kind of singularity in spacetime, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which spacetime is not locally Minkowskian under any coordinate transfor-mation. In particular, at such singularities, delta function sources in the second derivatives of the gravitational metric tensor exist in all coordinate systems, but due to cancelation, the Riemann curvature tensor remains uniformly bounded.

References:
[1] W. Israel, Singular hypersurfaces and thin shells in general relativity, Il Nuovo Cimento, Volume XLIV B no. 1 (1966), pp. 1-14.
[2] M. Reintjes and B. Temple, Points of General Relativistic Shock Wave Interaction are ”Regularity Singularities” where Spacetime is Not Locally Flat, Proc. R. Soc. A (accepted), arXiv:1105.0798.

Joint work with: (John), Blake Temple (University of California - Davis).

Abstract: Although predictions of general relativity have been confirmed in many experiments, the influence of gravity on quantum systems has only been tested in the Newtonian limit of the theory. Here we discuss a quantum interference experiment that can probe the interplay between quantum mechanics and general relativity. We propose testing general relativistic time dilation with a single "clock" in a superposition of two paths in space-time, along which time flows at different rates. We show that the interference visibility in such an experiment will decrease to the extent to which the path information becomes available from reading out the time from the "clock". For shorter time dilation the effect of gravity will result in a relative phase shift, observed so far only with massive particles. We consider implementation of the "clock" in evolving internal degrees of freedom of a massive particle and, alternatively, in the position of a photon (in which case the time dilation manifests itself through the Shapiro delay - slow down of light passing close to a massive body). We discuss under which conditions such interferometric experiments can only be explained if both general relativity and quantum mechanics apply. Their experimental feasibility is analyzed and we conclude that for photons the observation of the gravitationally induced phase shift is within reach of current technology.

Place: Common room, 1st floor.

Lunch seminar. Place: Common room, 1st floor.

Abstract: The Effective Field Theory approach can be employed to derive the Hamiltonian of a
gravitationally bound binary system. We show how the post-Newtonian (PN) approximation to
General Relativity can be neatly accomodated in a field theoretical framework as first
proposed by Goldberger and Rothstein, and how the standard tools developed for quantum field
theory (as for instance the Feynmann path integral and the renormalization group flow) can
be helpful in treating the classical 2-body problem in General Relativity. We show how the
3PN Hamiltonian has been reproduced via an algorithm implemented in Mathematica and report
about the progress towards the computation of the 4PN Hamiltonian.

Abstract: We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth globally hyperbolic space-times. Then we turn to the case where the metric is non-smooth and present a local as well as a global existence and uniqueness result for a large class of Lorentzian manifolds with a weakly singular, locally bounded metric in Colombeau's algebra of generalized functions.

Abstract: The aim of the talk is to explain how a lower bound on the Ricci curvature of a globally hyperbolic Lorentzian manifold implies an upper bound on areas and volumes of timelike geodesic spheres and balls. Afterwards, these results are used to give a new proof of Hawking's singularity theorem.

Abstract: I will discuss a class of curves in the Reissner-Nordstroem spacetime possessing special conformal properties. Like conformal geodesics in vacuum spacetimes, these curves provide, under suitable circumstances, a canonical conformal factor which can be read from the data of the curve. I will show that a congruence of these curves covers the whole of the outer domain of communication of the Reissner-Nordstroem spacetime in both the extremal and non-extremal cases. Finally, I will show how these c urves can be used to construct a generalisation of Gaussian coordinates by means of which one can evaluate (numerically) a conformal representation of the Reissner-Nord stroem spacetime.

Lunch seminar, common room, 1st floor.

Abstract: I give an introduction to recent developments in 3-dimensional classical and quantum gravity, including novel AdS_3/CFT_2 constructions. I then focus on a particular development, namely the "bootstrap" construction of all stationary axi-symmetric solutions of 3-dimensional Einstein gravity with a self-interacting scalar field, with particular focus on asymptotically flat and (A)dS solutions.

Abstract: A proof of decay estimates for test fields with non-zero spin, eg. Maxwell and linearized gravity, on the Kerr background is an important step towards understanding the black hole stability problem. Fields with non-zero spin on Kerr admit non-radiating modes which must be eliminated in order to prove decay. In this talk I will discuss the relation between conserved charges and hidden symmetries for linearized gravity on Minkowski space and vacuum spaces of Petrov type D and outline the application of these ideas in proving estimates for the higher spin fields on the Kerr background.

Place: Common room 1st floor. Lunch seminar.

Abstract: Within the cosmological framework and the observational evidence for the formation of first galaxies twelve billion years ago we quantitatively investigate galaxy evolution using the largest ground-based observatories and powerful space-based satellites. We focus on measureing physical parameters via spectroscopy at the Very Large Telescope of the European Southern Observatory and high-resolution imaging with the Hubble space telescope. With these data we investigate the evolution in mass, kinematics, structure, stellar populations and star formation activity of galaxies out to redshift z=1. We probe galaxies in all environments from the isolated field, over galaxy groups to clusters of galaxies. Our spectroscopy allows the determination of internal kinematics and the construction of scaling relations between dark and luminous matter. From two-dimensional velocity fields we quantify kinematic distortions, which we combine with a structural analysis using our Hubble images and a stellar population study based on spectral lines and multicolor photometry.  To assess possible interaction mechanisms we directly compare our observations with N-body/SPH simulations of different processes.  With our comprehensive combination of data, models, and theory, we explore the main drivers of galaxy formation and evolution.

Abstract: If a system of conservation equations admits a so-called convex extension, it can be written in symmetric hyperbolic form. In addition there is in this case available a body of results concerning existence and uniqueness of weak ("entropy"-) solutions. We point out a class of theories, which include ideal relativistic hydrodynamics as a special case, which naturally give rise to a system of conservation equations with a convex extension.

This is part of joint work with Philippe LeFloch.

Note the exceptional location: Erwin Schroedinger Institute and unusual time.

Abstract: In this talk I will overview the implications of a new established universal inequality A >= 8pi|J| between the area A and the angular momentum J of an axisymmetric (dynamical) black hole horizon. In particular I will explain the phenomenon of the formation of extreme Kerr-throats and a complete characterization of the geometry of (dynamical) horizons (a long standing problem) only from the difference A - 8pi|J|. The work, which is novel, has its roots and is very much related to developments done at the AEI.

Lunch seminar: Note the exceptional location: Erwin Schroedinger Institute and unusual time.

Abstract: We will explain how to use equivariant bifurcation theory to exhibit blow up solutions of the parabolic prescribed curvature equation whose blow up behaviors are only asymptotically self similar,  and break the O(3) symmetry of the problem in many possible ways as the bifurcation parameter related to the prescribed curvature varies.

Lunch seminar: Library, Währinger Straße 17, 1st floor.

Abstract: The problem of rescaling a pseudo--Riemannian metric to an Einstein metric is governed by a second order overdetermined PDE, which has a conformal covariance property by definition. I will explain how ideas from conformal geometry can be used to study this equation and its solutions. The equation has to be set up in such a way that an Einstein--rescaling is only obtained outside the zeros of the solution, so understanding the zero set is of particular interest. I'll discuss how comparison to the homogeneous model can be used to prove that zeros are either isolated or form embedded hypersurfaces. Near such a hypersurface, one obtains a so--called Poincare--Einstein metric, and any such metric arises in this way. These metrics are the basic ingredient for the AdS/CFT correspondence.
The equation governing Einstein rescalings is actually the simplest example of the first operator in a so--called BGG sequence, and I will briefly discuss what can be said about more complicated analogs.

Place: Währinger Straße 17, 1st floor, common room.

Place: Währinger Straße 17, 1st floor, common room.

Abstract: An alternative to the conventional semi-classical (or W.K.B.) ansatz for systems of nonlinear quantum oscillators leads, at lowest order, to an ‘inverted-potential-zero-energy’ (or ‘ipze’) variant of the usual Hamilton-Jacobi equation for the associated mechanics problem. Under suitable smoothness, convexity and coercivity hypotheses for the potential energy function we prove that this ‘ipze’ Hamilton-Jacobi equation has a smooth, globally defined, ‘fundamental solution’ S₀(x). Higher order quantum corrections to the wave functions (for both ground and excited states) can then be computed by integrating a set of linear transport equations and the natural demand for smoothness of these functions forces the corrections to the (ground and excited state) energy eigenvalues to take on explicit, computable values. For the special case of harmonic oscillators our expansions naturally truncate, reproducing the well-known exact solutions. For one-dimensional anharmonic oscillators, on the other hand, one can carry out the calculations explicitly using Mathematica. We describe results obtained for the quartic, sectic, octic and dectic oscillators and compare them with corresponding results derived via conventional Rayleigh/Schrödinger perturbation theory. In joint, ongoing work with Antonella Marini (Yeshiva and L’Aquila Universities) and Rachel Maitra (Albion College) we are applying the same ideas to nontrivial interacting quantum field theories including the phi⁴ scalar and Yang-Mills equations in Minkowski spacetime.

Abstract: One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of experimental evidence of quantum gravitational effects thus far is a major hindrance. Yet, the quantization of space-time itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme that allows an experimental test of this conjecture by probing directly the canonical commutation relation of the center of mass mode of a massive mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for tabletop experiments to test possible quantum gravitational phenomena.

Place: Währinger Straße 17, 1st floor, common room.

Abstract: This talk will be about two subjects related to the mass of asymptotically hyperbolic Riemannian manifolds. First, some results in the situation when the mass is small will be described. Second, special cases of the Penrose conjecture for asymptotically hyperbolic manifolds will be discussed. This is work in progress, joint with Romain Gicquaud and Anna Sakovich.

Abstract: We outline a proof of the rigidity statement in the positive mass theorem with charge incorporating the generalized Jang equation. This is joint work with M. Khuri.

Abstract: In the framework of Volumetric Geometry a Theory of Gravity is set up. It resembles Jordan-Brans-Dicke gravity, but the coupling to matter differs. There is viability with respect to the three classical tests, but with degeneracy in the JBD-coupling parameter. The evolution of the matter-dominated Cosmological Model is volume-preserving and for JBD-parameter omega=-4/3 already the vacuum solution describes a model with deceleration q=1/2 in the past and q=-1 in the future. The metric has positive spatial curvature and the corresponding Luminosity-Distance function follows closely the one for the Cosmological Concordance Model. There seems to be no need to introduce either "dark energy" or "dark matter".

Abstract: This will in essence be a (critical) review of arxiv.org/abs/1106.3743 , arxiv.org/abs/1109.5602 , and arxiv.org/abs/1109.6140 .

Abstract: I will discuss the construction of vacuum spacetimes filled with regular lattices of black holes and their application to the averaging and backreaction problems in cosmology.

Abstract: The celebrated Choquet-Bruhat Geroch theorem, of existence and uniqueness of maximal globally hyperbolic developments of general relativistic initial data, appears to require initial data in a Sobolev class which implies C³ differentiability of the solution. On the other hand, classical local existence and uniqueness works with H³+H² initial data, and recent studies by Klainerman and Rodnianski require even lower differentiability. One of the problem in matching the thresholds is classical Lorentzian causality theory, which requires C³ metrics.

In this talk we will revisit causality theory for Lorentzian metrics which are assumed to be merely continuous. We will discuss which standard facts of the theory become wrong for metrics which are not differentiable. In particular we will exhibit a surprising family of continuous metrics with light-cones which are not topological hypersurfaces.

The talk is based on joint work with James Grant and Greg Galloway.

Abstract: The Schoen-Yau Positive Mass Theorem states that an asymptotically flat 3 manifold with nonnegative scalar curvature has positive ADM mass unless the manifold is Euclidean space. Here we examine sequences of such manifolds whose ADM mass is approaching 0. We assume the sequences have no interior minimal surfaces although we do allow them to have boundary if it is a minimal surface as is assumed in the Penrose inequality. We conjecture that they converge to Euclidean space in the pointed Intrinsic Flat sense for a well chosen sequence of points. The Intrinsic Flat Distance, introduced in work with Stefan Wenger (UIC), can be estimated using filling manifolds which allow one to control thin wells and small holes. Here we present joint work with Dan Lee (CUNY) constructing such filling manifolds explicitly and proving the conjecture in the rotationally symmetric case.

Abstract: An auspicious strategy on the way to establish a global existence theorem for the characteristic Cauchy problem with data given on a light cone is to transform it into a local problem in a conformally rescaled spacetime, where Friedrich's conformal field equations form an adequate substitute to Einstein's field equations. As a prerequisite to prove local existence of a solution in some neighbourhood where the cone intersects Scri, all traces of the fields appearing in the conformal field equations (or some appropriate variation of them) on the cone need to be smoothly extendable across Scri. An investigation of this issue will be the main object of our talk.

Abstract: In this talk I present my current work on gravitational collapse in 2+1 dimensional Anti-de Sitter spacetime. It is work in progress, so I will focus on main ideas rather than give definitive results. Previous studies of the topic include an article by Matthew Choptuik and Frans Pretorius, as well as work by David Garfinkle and Carsten Gundlach investigating the nature of the critical solution.

Place: Währinger Straße 17, 1st floor, common room.

Abstract: We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an isotropic singularity. This family of solutions is `generic' in the sense that it depends on as many free functions as a general solution, i.e., without imposing any symmetry assumptions, of the Einstein-Euler equations.

Abstract: We consider several tensorial wave equations, specifically the equations of Maxwell, Yang-Mills, and Weyl fields, posed on a curved spacetime, and we establish energy inequalities under certain one-sided geometric conditions.

This talk is based on joint work with A. Burtscher (Vienna) and P. LeFloch (Paris VI, CNRS), contained in the preprint arxiv/1105.0168.

Abstract: The Corvino-Schoen method allows to glue locally and smoothly solutions of the relativistic constraints equations. In this talk I will show that the approach can be generalized to glue two elements in the kernel of certain underdetermined elliptic operators. For instance, one can glue two divergence-free vectors fields or two TT-tensors. A simple consequence is that on any Riemannian ball, the set of smooth TT-tensors with compact support is infinite dimensional.

Abstract: The issue concerning "dark matter" comes from Newtonian approximations for the full Newtonian N-body problem.  As shown, when combined with observed rotational velocities, this approach requires mass levels that are significantly larger than what has been observed. But, is this approximation method correct?  By using analytic properties of the Newtonian N-body problem to derive new relationships between rotational velocity and mass values, it is shown that the conflict is nowhere near as extreme as asserted in the literature.

Abstract: In my seminar I will discuss the black hole theory in spacetimes of dimension higher than four. The theory of the higher dimensional black holes is remarkably different and much richer than in four dimensions. In order to demonstrate that I will focus on the most interesting and important representative examples of higher dimensional black solutions, for example the black ring and the black Saturn.  Solution generating methods allowing us to construct various exact black hole solutions will be discussed briefly. Finally I will present the uniqueness theorem classifying the black solutions to the vacuum Einstein equations in five dimensions and its generalizations.

Abstract: I review the definition and the properties of Bartnik's definition of "quasilocal" mass for a bounded spatial region, and specialize to the case where the region is trapped. In a foliated spacetime, I show that the Bartnik mass of the trapped region is monotonic upon time evolution, and I discuss a possible connection of this result with weak cosmic censorship.

Abstract: We study the elastic deformations that appear due to tidal forces for an elastic sphere on a circular orbit around a gravitational centre, where gravity is considered to be given by either a Newtonian or a Schwarzschild background. We try to give both an existence/uniqueness theorem based on the implicit function theorem and to find explicit solutions to the linearized elastostatic equations.

Abstract: I review the definition and the properties of Bartnik's definition of "quasilocal" mass for a bounded spatial region, and specialize to the case where the region is trapped. In a foliated spacetime, I show that the Bartnik mass of the trapped region is monotonic upon time evolution, and I discuss a possible connection of this result with weak cosmic censorship.

Abstract: The Bianchi model is  a system of ODE's describing spatially homogeneous, anisotropic spacetimes. It admits a circle of equilibria called the Kasner circle. Orbits connecting pairs of equilibria are encoded in the Kasner map. It is conjectured that formal chains of such heteroclinic connections drive the asymptotical dynamics as  time is going to minus infinity, i.e. at the big bang singularity.

In their paper "The BKL Conjecture for spatially homogeneous Spacetimes", Reiterer and Trubowitz exhibit initial conditions whose trajectories follow  heteroclinic chains with less restrictions on their proximity to the Taub points than in previous results. In this talk, we will expose an overview of their proof and discuss the conclusion on the genericity question: their result covers generic heteroclinic chains, but not generic initial conditions of the full system.

Abstract: In General Relativity, the study of spacetimes with singularities, like black hole spacetimes or cosmological models with a big bang singularity, is a predominant subject. However, although it is known that singularities form in large classes of spacetimes, comparatively little is known about the structure of these `generic' singularities: How do the metric and the curvature that characterize the gravitational field behave close to a singularity? In this talk I will consider classes of spatially homogeneous cosmological models that possess singularities whose structure can be analyzed successfully. I will then argue that the dynamics of these models close to a singularity is the key to our understanding of generic spacelike singularities.

Place: ESI lecture hall.

Abstract: We explain how simple pre-geometric matrix models lead to "emergent" quantized space or space-time, equipped with an effective theory of gravity. Some aspects of the low-energy description are discussed, which besides an effective metric also involves a dynamical Poisson tensor. Certain preferred models can be expected to be well-behaved under quantization, thus providing a novel approach towards a quantum theory of gravity.

Abstract: Co-rotational wave maps from (3+1)-Minkowski space into the three-sphere are known to exhibit finite time blow up via self-similar solutions. Based on numerical investigation the self-similar ground state solution f₀, which is known in closed form, is supposed to describe the generic blow up behaviour of the system. We present a rigorous linear perturbation theory around f₀ and show that this solution is linearly stable if it is mode stable. Concerning the problem of mode stability, we prove nonexistence of eigenvalues with real parts larger than 1=2. This in combination with other available numerical and analytic results strongly suggests the nonexistence of unstable modes. The results that will be presented in this talk are based on recent work in collaboration with R. Donninger and P.C. Aichelburg.

Place: Common room, Waehringerstrasse 17, 1st floor.

Abstract: After reviewing the notion of an initial data set for the Einstein equations, we prove the existence of a certain class of initial data sets with one asymptotically flat and one asymptotically cylindrical end. We also discuss the uniqueness of the obtained solutions.

Abstract: Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop-Gromov relative volume monotonicity theorem and Guenther's volume comparison theorem.

Abstract: We discuss high order absorbing constraint preserving boundary conditions for the Z4 formulation of general relativity coupled to the moving puncture family of gauges. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we prove well-posedness of the initial boundary value problem with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions in constraint preservation and absorption is presented in spherical symmetry.

Abstract: The extension of the canonical formalism of Arnowitt, Deser and Misner from point-masses to spinning objects is a long standing problem in general relativity. Two independent approaches to a solution of this problem are given in this talk. The first approach is based on an action functional and is similar to the original derivation of Arnowitt, Deser and Misner for non-spinning objects. This action approach currently covers the pole-dipole approximation of self-gravitating extended bodies to linear order in spin. Similarities to the canonical formulation of (classical) Dirac fields coupled to gravity are pointed out. The second approach is based on an explicit order-by-order construction of the canonical formalism within the post-Newtonian approximation scheme. Here the generators of global rotations and translations play a crucial role. As an application, spin contributions to next-to-leading order in the post-Newtonian approximation scheme are presented. The canonical formulation at higher orders in spin, which includes quadrupole deformation effects, is discussed.

Abstract: I talk about ongoing joint work with Bernd Schmidt on constructing models for self-gravitating, elastic bodies close to a spherical solution.

Note: Room 118, Währinger Straße 17, 1st floor.

Abstract: My work at the moment centres around adapting analytical and geometrical techniques from Riemannian geometry to the study of problems in Lorentzian geometry. In this talk, I will give a status report on joint work with P.G. LeFloch (CNRS and Paris VI), in which we use comparison techniques, such as the Rauch comparison theorem and Hessian comparison theorem, to estimate the null injectivity radius on a Lorentzian manifold. This work gives a more geometrical setting for some recent work of Klainerman and Rodnianski on null injectivity radius estimates.

Abstract: Understanding the apparent acceleration of the universe as indicated by supernova data, and confirmed by other data in a cosmic concordance model, is a major preoccupation of present day cosmology. It is also a major puzzle for theoretical physics, as we have no fundamental explanation of why such a cosmological constant or "quintessence" field should exist. I will compare three possible explanations of the observations: (i) it is due to a cosmological constant causing an accelerated epoch in a Friedmann-Lemaitre model, and with the very small magnitude of the force (in fundamental terms) justified by a multiverse explanation, as proposed by Weinberg, Rees, and others; (ii) it is due to backreaction effect caused by the granular nature of the universe, as proposed inter alia by Kolb, Matarrase, and Wiltshire; (iii) it is caused by a Hubble-scale inhomogeneity - a violation of the Copernican Principle, as proposed by Celerier and many others. I will claim that the latter is a viable and testable option, and so must be treated as seriously as other explanations.

Abstract: I will discuss the Cauchy problem for the Einstein equations with data on a light-cone.

Abstract: I will outline recent progress that has been made towards the classification of black holes in higher dimensions. This will include (a) setups where the symmetry of the solution is assumed to be $R x T^{D-3}$, where $D$ is the number of spacetime dimensions (b) recent results restricting the possible horizon topology of stationary black holes without further symmetry assumptions and (c) classification of the geometry in the near-horizon region extremal black holes.

Abstract: We exploit information from the near horizon geometry of a regular degenerate black hole to extend the proof of uniqueness for non-degenerate Kerr-Newman solutions to the degenerate case.

Abstract: For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, though the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.

Note: Room 118, Währinger Straße 17, 1st floor.

Abstract: The world-wide network of large laser interferometers is on the verge of directly detecting gravitational waves (GW) for the first time. A potential candidate for such a detection is the signal of a coalescing binary black hole (BBH). Identifying its signature in the noise-dominated spectrum of a GW detector relies on the comparison to theoretically predicted template waveforms, and current advances in analytical and numerical relativity make it possible to describe all parts of the inspiral-merger-ringdown process the black holes undergo.