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Speaker: Emanuele Berti, Johns Hopkins UniversityTitle: Black Hole SpectroscopyVenue: VirtualAbstract: According to general relativity, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as, say, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2)… |
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Speaker: Qian Wang, University of OxfordTitle: Rough solutions of the $3$-D compressible Euler equationsVenue: VirtualAbstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \omega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$. The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational case, i.e $\omega=0$, which is known to be optimal for $s>2$. At the opposite extreme, in the incompressible case, i.e. with a constant density, the result is known to hold for $\omega\in H^s$, $s>3/2$ and fails for $s\le 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be $(v,\varrho, \omega) \in H^s\times H^s\times H^{s’}$, $s>2,… |
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Speaker: Prof. Arick Shao (Queen Mary University of London)Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimesVenue: VirtualAbstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture. In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. This is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas). |
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Speaker: David Fajman (University of Vienna)Title: The Einstein-flow on manifolds of negative curvatureVenue: VirtualAbstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions. |
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Speaker: Achilleas PorfyriadisTitle: Extreme Black Holes: Anabasis and Accidental SymmetryVenue: virtualSpeaker: Achilleas Porfyriadis, Harvard Black Hole Initiative Title: Extreme Black Holes: Anabasis and Accidental Symmetry Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2. |
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Speaker: Shiraz Minwalla (Tata Institute of Fundamental Research, Mumbai)Title: Black Hole dynamics at Large DVenue: VirtualAbstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime. |
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Speaker: Tin Yau TsangTitle: Dihedral ridigity and massVenue: VirtualAbstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass). |
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Speaker: Xinliang An, University of SingaporeTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formationVenue: VirtualAbstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result… |
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Speaker: Professor Geoffrey Compére, Université Libre de BruxellesTitle: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-mergerVenue: VirtualAbstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions. |
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Speaker: Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric SpacetimesVenue: VirtualAbstract: The analysis of global structure of the Einstein equations for general relativity, in the context of the initial value problem, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome, in order to alleviate the problem. It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational, fixed-point free, spatial U(1) isometry group are globally well-posed. In our previous works, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data. In this talk, after discussing some preliminaries and background, we shall discuss about yet another structure of the U(1) symmetric… |
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Speaker: Siyuan Ma, Sorbonne UniversityTitle: Sharp decay for Teukolsky equation in Kerr spacetimesVenue: VirtualAbstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components, $s=0, \pm 1, \pm 2$ corresponding to the scalar field, the Maxwell field, and the linearized gravity, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes. |
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Speaker: Elena Giorgi, Columbia UniversityTitle: The stability of charged black holesVenue: VirtualAbstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole, where the interaction between the radiations prevents the separability in modes. |
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Speaker: Xiaoning Wu, Chinese Academy of SciencesTitle: Causality Comparison and Postive MassVenue: VirtualAbstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new, substantially simple, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity |
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Speaker: Jorge Santos, University of CambridgeTitle: The classical interior of charged black holes with AdS asymptoticsVenue: VirtualAbstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior. The spacetime ends at a… |
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Speaker: Roberto Emparan, University of BarcelonaTitle: The Large D Limit of Einstein’s EquationsVenue: VirtualAbstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers… |
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Speaker: Jiong-Yue Li, Sun Yat-Sen UniversityTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equationsVenue: VirtualAbstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles. We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models. |
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Speaker:Title: General Relativity 2021-22Venue: VirtualDuring the 2021–22 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Aghil Alaee, Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend, please fill out this form. The schedule below will be updated as talks are confirmed. Spring 2022 Date Speaker Title/Abstract 2/10/2022 Tin Yau Tsang (UC Irvine) Title: Dihedral ridigity and mass Abstract: To characterise scalar curvature, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk, we will… |
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Speaker: Zhongshan AnTitle: Static vacuum extensions of Bartnik boundary data near flat domainsVenue: VirtualAbstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan… |
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Speaker: Alex LupsascaTitle: 9/24/2021 General Relativity SeminarVenue: VirtualTitle: On the Observable Shape of Black Hole Photon Rings Abstract: The photon ring is a narrow ring-shaped feature, predicted by General Relativity but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice, near-term interferometric observations may be limited to the visibility amplitude alone, which contains incomplete… |
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Speaker: Igor RodnianskiTitle: 9/17/2021 General Relativity SeminarVenue: VirtualTitle: Stable Big Bang formation for the Einstein equations Abstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature, going back more than 50 years, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos. |