
Speaker: Uri KolTitle: Duality in Einstein’s GravityVenue: CMSA Room G10General Relativity Seminar Speaker: Uri Kol, CMSA Title: Duality in Einstein’s Gravity Abstract: ElectricMagnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more. 

Speaker: Marcelo DisconziTitle: Generalrelativistic viscous fluidsVenue: virtualGeneral Relativity Seminar Speaker: Marcelo Disconzi, Vanderbilt University Title: Generalrelativistic viscous fluids Abstract: The discovery of the quarkgluon plasma that forms in heavyion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quarkgluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quarkgluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quarkgluon plasma. For more than two decades, the community has intensely studied the quarkgluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quarkgluon plasma behaves essentially like a relativistic liquid… 

Speaker:Title: A scalecritical trapped surface formation criterion for the EinsteinMaxwell systemVenue: CMSA Room G10General Relativity Seminar Speaker: Nikolaos Athanasiou Title: A scalecritical trapped surface formation criterion for the EinsteinMaxwell system Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang… 

Speaker: Professor Pau FiguerasTitle: The GregoryLaflamme instability of black strings revisitedVenue: CMSA Room G10General Relativity Seminar Title: The GregoryLaflamme instability of black strings revisited Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the GregoryLaflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string. 

Speaker: Harvey ReallTitle: The second law of black hole mechanics in effective field theoryVenue: CMSA Room G10General Relativity Seminar Speaker: Professor Harvey Reall (University of Cambridge) Title: The second law of black hole mechanics in effective field theory Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs. Video 

Speaker: Allen Fang, Sorbonne UniversityTitle: A new proof for the nonlinear stability of slowlyrotating Kerrde SitterVenue: VirtualAbstract: The nonlinear stability of the slowlyrotating Kerrde Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowlyrotating Kerrde Sitter spacetimes that avoids frequencyspace techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability. 

Speaker: Jinhua Wang, Xiamen UniversityTitle: Future stability of the $+$ Milne model for the EinsteinKleinGordon systemVenue: VirtualAbstract: We study the small perturbations of the $1+3$dimensional Milne model for the EinsteinKleinGordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete. For the proof, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the BianchiKleinGordon equations. Moreover, we treat the BianchiKleinGordon equations as evolution equations and establish the energy scheme in the sense that we only commute the BianchiKleinGordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument. 

Speaker: Chao Liu (HUST)Title: Global existence and stability of de Sitterlike solutions to the EinsteinYangMills equations in spacetime dimensions n≥Venue: VirtualAbstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of nonlinear perturbation of de Sitterlike solutions to the EinsteinYangMills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) EinsteinYangMills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang. 

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)… 

Speaker: Qian Wang, University of OxfordTitle: Rough solutions of the $$D compressible Euler equationsVenue: VirtualAbstract: I will talk about my work on the compressible Euler equations. We prove the localintime 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 SmithTataru 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 BourgainLi. 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,… 

Speaker: Prof. Arick Shao (Queen Mary University of London)Title: Bulkboundary correspondence for vacuum asymptotically Antide Sitter spacetimesVenue: VirtualAbstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Antide 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 onetoone correspondence between aAdS solutions of the Einsteinvacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stressenergy 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). 

Speaker: David Fajman (University of Vienna)Title: The Einsteinflow 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 CMCEinstein flow. We will briefly review the AnderssonMoncrief 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+1dimensions. 

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 nearhorizon region of black holes near extremality is universally AdS_2like. In this talk I will concentrate on the simplest example of AdS_2 x S^2 as the nearhorizon of (near)extreme ReissnerNordstrom. 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 ReissnerNordstrom 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 onshell large diffeomorphism of AdS_2. 

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. 

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). 

Speaker: Xinliang An, University of SingaporeTitle: Low regularity illposedness for D elastic waves and for D ideal compressible MHD driven by shock formationVenue: VirtualAbstract: We construct counterexamples to the local existence of lowregularity 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 illposed 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 illposedness 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 lowregularity illposedness result… 

Speaker: Professor Geoffrey Compére, Université Libre de BruxellesTitle: Kerr Geodesics and Selfconsistent match between Inspiral and TransitiontomergerVenue: VirtualAbstract: The twobody 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 selfforce. I will describe its quasicircular inspiral motion in the radiation timescale expansion. I will describe in parallel the transitiontomerger 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. 

Speaker: Nishanth Gudapati, Clark UniversityTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U() 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, fixedpoint free, spatial U(1) isometry group are globally wellposed. 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 Einsteinwave 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… 

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. 

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 energymomentum tensor for the system. Finally, I will show how this physicalspace approach is resolutive in the most general case of KerrNewman black hole, where the interaction between the radiations prevents the separability in modes. 