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 https://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 http://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.
Wednesday, October 24, 14:15, Ettore Minguzzi (Pisa): Lightlike lines and time functions in general relativity
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."