Talk archive

• Wednesday, January 22^nd, 14:15
  Speaker: David Kubiznak (Charles University Prague): Remarkable symmetries of rotating black holes

We identify It is well known that the Kerr geometry admits a non-trivial Killing tensor and its square root' known as the Killing-Yano tensor. These two objects stand behind the Carter's constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object -- the principal Killing-Yano tensor – generates a tower of explicit and hidden symmetries responsible for integrability of  geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes  described by the ‘magic square' version of the Lense-Thirring solution, giving rise to a geometrically preferred pacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.
 

• Wednesday, February 19^th, 14:15
  Speaker: Cedric Deffayet (Paris): Ghosts without runaway instabilities

I will discuss simple mechanical models with a ghost (i.e. a mode with a negative kinetic energy) interacting with a positive energy degree of freedom, and yet, the phase-space motion can be shown analytically and numerically to be fully stable thanks to integrability. Extensions to field theories will also be discussed.
 

• Wednesday, 26 March 2025, 2:15 p.m., Seminarraum A, Währinger Straße 17, 1090 Vienna, 2nd floor
  Speaker: Marco Bruni (University of Portsmouth): Nonlinear  Relativistic Structure Formation  in  ƛCDM

In this talk I will give an overview of work on nonlinear structure formation in the the standard model of cosmology, ƛCDM, assuming General Relativity (GR). Starting from briefly presenting a post-Friedmann approximation (similar to post-Minkowski, but on a cosmological background and assuming small peculiar velocities), I will show how at leading order the  gravito-magnetic effect (AKA frame-dragging)  can be extracted from standard Newtonian N-body simulations, as well as from N-body simulations with GRAMSES, an approximate GR code.  I will then present full-GR simulations of a toy-model “cosmic web” of over-densities,   voids and filaments with the Einstein Toolkit fluid code,  showing how  the first shell-crossing at peaks of over-densities is very well predicted by the simple "top hat" model, while in the formation of the cosmic web a role is played by gravito-magnetism, especially around filaments.  In the last part of the talk I will illustrate some work in progress, some aimed at extending the work on frame-dragging on smaller galactic scales, some aimed at understanding to what extent relativistic effects can play a role during collapse and past the first shall crossing and virialization. I will conclude with an  outline of possible future work.

• Wednesday, December 4^th, 14:15 [via Zoom]
  Speaker: Pedro Cunha (University of Aveiro): Hypershadows: Imaging 5 dimensional black holes

What does a black hole look like? In 1+3 spacetime dimensions, the optical appearance of a black hole is a bidimensional region  in the observer's sky often called the black hole shadow, as supported by the EHT observations. In higher dimensions this question is more subtle and observational setup dependent. Previous studies considered the shadows of higher dimensional black holes to remain bidimensional. We argue that the latter should be regarded as a tomography of a higher dimensional structure, the hypershadow, which would be the structure  "seen" by higher dimensional observers. As a case study we consider the cohomogeneity-one (equal-spins) Myers-Perry black hole in 1+4 dimensions, and compute its tridimensional hypershadow.
 

• Wednesday, November 20^th, 14:15
  Daniel Grumiller (TU Wien): NEC angle in critical collapse

We identify a new critical parameter in Choptuik's gravitational collapse: the angle at which null energy condition (NEC) saturation lines intersect at the center of the critical spacetime. These NEC lines coincide with regions of vanishing curvature, dividing spacetime into stripes of positive and negative curvature. By numerically solving Choptuik's original system we find the NEC angle to be \alpha=0.64 (about 37 degrees) and analytically derive \alpha=2\arccot(D-1) for any spacetime dimension D>3.
 

• Wednesday, November 27^th, 14:15
  Marios Christodoulou (IQOQI Vienna): Frontiers in Table Top Quantum Gravity

Table Top Quantum Gravity nowadays colloquially refers to a forming interdisciplinary field that includes diverse contributions from theorists, experimentalists and philosophers alike across a  range of disciplines from spacetime physics to quantum technologies. I discuss some of my contributions to the debate surrounding this nascent research field, while giving an overview of recent ideas and foundational issues that have arisen.
 

• Wednesday, November 13^th, 14:15
  Adam Cieślik (Jagiellonian University of Krakow): Monte Carlo simulation of a planar accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole

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.
 

• Wednesday, November 6^th, 15:00, On-line via ZOOM
  Alexander Watson (University of Minnesota): Wave-packet dynamics in locally periodic media

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.
 

• Wednesday, October 16^th, 14:15, Seminarraum A
  Anxo Biasi (Ecole Normale Superieure-PSL): Turbulent Cascades and condensation in Hamiltonian systems

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).
 

• Wednesday, October 9^th, 14:15, Seminarraum A
  Dennis Rätzel (ZARM, Bremen): Non-linear media in weakly curved spacetime: optical solitons and probe pulses for gravimetry

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)
 

• Wednesday, September 14^th, 14:00, Seminarraum A, Währinger Strasse 17, 2nd Floor
  David Hilditch (Lisbon, CENTRA): The Black Hole Threshold

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.
 

• Wednesday, September 11^th, 11:00, Erwin-Schrödinger-HS, Boltzmanngasse 5, 5th floor
  Gilbert Weinstein (Ariel U): The mass angular momentum inequality

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.
 

• Tuesday, July 9^th, 12:30, Library, Währinger Strasse 17, 2nd Floor
  Mario Hudelist (University of Vienna): Space-time curvature-induced corrections to Rytov's law in optical fibers

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.
 

• Wednesday, July 3^rd, 14:00, Seminarraum A
  Diego Silimbani (SISSA): Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on S3

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.
 

• Wednesday, May 22^nd, 14:15, ESI, Boltzmanngasse 9A, main lecture hall
  Filip Ficek (Vienna): Dynamics of conformal scalar field in asymptotically-AdS black hole spacetimes

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.
 

• Wednesday, May 15^th, 14:15, ESI
  Arthur Touati (IHES): Initial data for stability theorems in general relativity

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.
 

• Wednesday, May 8^th, 13:45, via zoom (link posted separately)
  Seven Hirsch (IAS): Initial data sets with vanishing mass are contained in pp-waves.

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.

-> video of the talk, -> audio of the talk

• Friday, May 3^rd, 11:45, Seminarraum A
  David Fajman (U of Vienna): Shock formation in cosmological fluids 

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.
 

• Tuesday, April 30^th, 13:00, Seminarraum A
  Abhiram Kidambi (MPI for Mathematics): Characterization of rational SCFTs: Complex Multiplication, Mirror Symmetry and Hodge Theory 

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.
 

• Wednesday, April 24th, 14:15, via zoom
  Martin Reiris (Montevideo): Static 3+1 vacuum black holes that cannot be put into stationary rotation

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.

-> video of the talk, -> audio of the talk

• Wednesday, April 17th, 14:15, ESI Main Lecture Hall
  Leonhard Kehrberger (Leipzig): The Case Against Smooth Null Infinity and the Persistence of Polyhomogeneity

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.
 

• Tuesday, April 16th, 13:00, Seminarraum A
  Felix Willenborg (University of Bremen): Wave optical image formation of exact scalar wave scattering in Kerr-de Sitter spacetime

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.
 

• Wednesday, April 10th, 14:15, Seminarraum A
  Mikołaj Korzyński (Center for Theoretical Physics, Polish Academy of Sciences): Weighing spacetime along the line of sight using times of arrival of electromagnetic signals

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.
 

• Wednesday, March 20th, 14:15
  Seminarraum A Marius Oancea (U of Vienna): Gravitational memory effects for particles and wave packets

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.
 

• Friday, March 15th, 14:30, Library Währingerst. 17
  Robert Beig (U of Vienna): The ADM decomposition 'done right'

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.
 

• Wednesday, March 13th, 14:15, Seminarraum A
  Marc Mars (U of Salamanca): On staticity of bifurcate Killing horizons

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.
 

• Monday, January 29th, 12:30, Lunch seminar library A
  Helmuth Urbantke (U of Vienna): Lexell's circle and an exercise about Dirac's magnetic monopole
  
   
• Wednesday, January 24th, 14:15, Seminarraum A
  Wan Cong (U of Vienna): On characteristic gluing

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]
 

• Wednesday, January 17^th, 14:15, Seminarraum A CANCELLED TO A DATE TBD
  Maciej Maliborski (U of Vienna): Dynamics of nonlinear scalar field with Robin boundary condition on the Schwarzschild--Anti-de Sitter background 

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.

• Friday, December 15^th, 13:00, Library Währingerstraße 17, 1st floor
  Andrea Nuetzi (Stanford U): Maurer-Cartan perturbation theory and scattering amplitudes in general relativity

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.
 

• Wednesday, December 13^th, 14:15, Seminarraum A
  Marcus Sperling (U of Vienna): Symplectic Singularities in Physics: Their Origins and Significance

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.
 

•  Wednesday, December 6^th, 14:15, Seminarraum A
  Jerzy Lewandowski (Warsaw): Conformally invariant approach to asymptotically de Sitter spacetimes 

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.
 

• Wednesday, November 8^th, 14:15
  Abraham Harte (Dublin City U): Constraining extended-body motion in general relativity

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.
 

• Wednesday, November 15^th, 14:15, Seminarraum A
  Tiberiu Harko (Babes-Bolyai U): From the Weyl-Schrödinger connection to the accelerating Universe - extending Einstein's gravity via a length preserving nonmetricity 

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.
 

• Thursday, November 16^th, 15:15, Seminarraum A
  Helmut Friedrich (AEI Potsdam): Cosmological models: Hierarchies of asymptotic behaviour 

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.
 

• Wednesday, November 22^nd, 14:15, Seminarraum A
  James Lucietti (Edinburgh): Rigidity of extremal horizons and black hole uniqueness 

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.
 

• Monday, November 27^nd, 13:00, Lunch Seminar, library Währingerstraße 17, first floor
  Florian Ecker (TU Wien): Carroll black holes 

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.
 

• Wednesday, November 29^th, 14:15, Seminarraum A
  Hakan Andreasson (Goteborg): Compactness of minimizing sequences for the Einstein-Vlasov system 

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.
 

• Wednesday, October 25^th, 14:15 Vera seminar room, Währingerstraße 17, Hoftrakt
  Albert Huber (Vienna): Quasilocal corrections to Bondi's mass loss formula and dynamical horizons

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.
 

• Friday, October 13^th , 13:00, Lunch Seminar, library Währingerstraße 17, first floor
  Finnian Gray (Vienna): Love symmetry in higher-dimensional rotating black hole spacetimes

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.
 

• Wednesday, October 18^th , 14:15 Vera seminar room, Währingerstrasse 17, Hoftrakt
  Walter Simon (Vienna): Uniqueness of asymptotically flat vacuum instantons with a cyclic isometry group

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.
 

• Wednesday, October 11^th
  Jorge Santos (Cambridge): Static Black Binaries in de Sitter

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.

-> video of the talk, -> audio of the talk

• Monday, October 9^th
  Albachiara Cogo (Vienna and Tuebingen): Maximal Surfaces over exterior domains and approximation of Null Hypersurfaces

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.
 

• Wednesday, October 4^th
  Matt Choptuik (UBC): Gravitational Critical Collapse Beyond Spherical Symmetry

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.

-> video of the talk, -> audio of the talk

• Friday September 29^th
  Piotr Chrusciel (Vienna) Energy in 2+1 dimensional spacetimes
  
   
• Tuesday, September 5^th
  Claudio Paganini (University of Regensburg): The Causal Compatibility Conjecture and its Implication on Time Travel

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.
 

• Wednesday, July 19^th
  Andrew Eberhardt (Stanford): The classical field approximation for Ultra Light Dark Matter

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.
 

• Tuesday, July 4^th, Join seminar Maths, Gravitational Physics and ESI (ESI Seminar room)
  Florian Johne (Columbia): Intermediate curvature and a generalization of Geroch's conjecture

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.
 

• Wednesday, June 21^st, Lunch seminar 12:00, Seminarraum A
  Anxo Biasi (Jagiellonian University): de Sitter bubbles from anti-de Sitter fluctuations

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.
 

• Thursday, June 22^th
  Jörg Hennig (TU Clausthal): The conformally invariant wave equation near the cylinder at spacelike infinity on a Schwarzschild background

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.

-> video of the talk, -> audio of the talk

• Thursday, June 15^th
  Camille Bonvin (U of Geneva): Measuring the distortion of time with large-scale structure

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.

-> video of the talk, -> audio of the talk

• Friday, June 2^nd, Lunch seminar 13:00, Seminarraum A
  Thomas Mieling (Vienna): Fiber Optics in Curved Space-Times: Effects of Lapse and Shift

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.
 

• Thursday June 1^st, 15:30, Seminarraum A
  Oliver Hahn (Astrophysics, Vienna): Large-scale structure cosmology at the interface of numerical and analytical techniques

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.
 

• Thursday, May 25^th, 15:30
  Yakov Shlapentokh-Rothman (Toronto): Twisted Self-Similarity and the Einstein Vacuum Equations

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.

-> video of the talk, -> audio of the talk

• Wednesday, May 24^th, Lunch seminar 13:00
  Roman Brem (Univ. Vienna): Visibility of Marginally Outer Trapped Surfaces

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.
 

• Thursday, May 4^th, 15:30
  Dennis Rätzel (Berlin) : Testing the gravity-quantum interface with optomechanics and quantum memories

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

-> video of the talk, -> audio of the talk

• Thursday, April 27^th, 15:30
  Abraao Mendes (Maceio, Brasil): Some rigidity results for compact initial data sets

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.
 

• Monday, April 24^th, 13:00 Lunch Seminar
  Marius Oancea (Vienna) : Wigner functions in curved spacetime

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.
 

• Thursday, April 20^th, 15:30
  Marcus Khuri (Stony Brook) : Black lenses in Kaluza-Klein matter

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.

-> video of the talk, -> audio of the talk

• Thursday, March 30^th, 15:30
  Thomas Mieling (Vienna): Polarization transport in optical fibers beyond Rytov’s law

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]
 

• Wednesday, March 29^th, 14:00 Lunch Seminar
  Andras Vasy (Stanford): Microlocal analysis near null infinity on asymptotically flat spacetimes

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.
 

• Monday, March 27^th, 13:00 Lunch Seminar
  Piotr Chrusciel (Vienna): Noether charges on light cones for field theories on (A)dS backgrounds

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.
 

• Thursday, March 23^rd, 15:30
  Domenico Giulini (Hannover): Are there gravitons? And how do you couple quantum matter to classical gravity?

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

-> video of the talk, -> audio of the talk

• Thursday, March 16^th, 15:45
  Christoph Kehle (ETH Zurich): Retiring the third law of black hole thermodynamics

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).
 

• Friday, March 10^th, 15:30 Lunch Seminar
  Piotr Chrusciel (Vienna): Gluing variations

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]
 

• Thursday, March 9^th, 15:30
  Stefan Hollands (Leipzig) : Black Hole Interiors

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.
 

• Thursday, March 2^nd, 15:30
  Maximilian Ofner (Vienna) : Structure formation in slowly expanding cosmological fluids

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.
 

• Thursday, February 23^rd, 15:30
  Finnian Gray (Vienna) : Hidden Symmetries and Separability in Rotating Black Hole Spacetimes

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.
 

• Thursday, February 2^nd, 14:00
  Filip Ficek (Vienna) : Nonlinear Schrödinger equations with trapping potentials in higher dimensions

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.
 

• Thursday, January 26^th, 15:30
  Peter Hintz (ETH Zuerich): Gluing small black holes into initial data sets

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.

-> video of the talk, -> audio of the talk

• Thursday, January 19^th, 15:15
  M. Maliborski (Vienna): Instability of a massless scalar field confined in a perfectly reflecting spherical cavity

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.

-> video of the talk, -> audio of the talk

• Tuesday, January 17^th, 12:00 Lunch Seminar
  Juan A. Valiente Kroon (Queen Mary, University of London): Dain's invariant for black hole initial data

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.
 

• Thursday, January 12^th, 15:15
  Stefan Czimek (Leipzig): Obstruction-free gluing for the Einstein equations

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.
 

• Wednesday, January 11^th, 14:15 Lunch Seminar
  Frank Schindler (Vienna): Dynamical friction in FDM halos

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 theory.