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: TBA
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 R^{5}. 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’ S_{0}(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 phi^{4} 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 C^{3 }differentiability of the solution. On the other hand, classical local existence and uniqueness works with H^{3}+H^{2} 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 C^{3} 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: I will discuss the Einstein's field equations of general relativity when weak regularity only is assumed on the initial data set and, therefore, on the spacetime itself. The curvature must then be understood in the weak sense, and the formulation of the initial value problem for the Einstein equations must be revisited. I will present here results on the existence and global geometry of certain class of spacetimes with symmetry. For recent preprints, see: philippelefloch.org.
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 f_{0}, 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 f_{0} 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.