During the 2022–23 academic year, the CMSA will be hosting a seminar on General Relativity, organized by Jue Liu, Daniel Kapec, and Puskar Mondal. This seminar will take place on Thursdays at 10:30 am – 11:30 am (Eastern time). After daylight savings time, the seminar time will be moved 9:30 am –10:30 am (Eastern Time). To learn how to attend, please fill out this form. The meetings will take place in Room G10 at the CMSA, 20 Garden Street, Cambridge MA 02138, and some meetings will take place virtually on Zoom or be held in hybrid formats. The schedule will be updated as talks are confirmed.

CMSA COVID-19 Policies

• October 06, 2022 10:30 AM
Speaker: Uri Kol
Venue: CMSA Room G10

General Relativity Seminar Speaker: Uri Kol, CMSA Title: Duality in Einstein’s Gravity Abstract: Electric-Magnetic 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.

• September 29, 2022 10:30 AM
Speaker: Marcelo Disconzi
Venue: virtual

General Relativity Seminar Speaker: Marcelo Disconzi, Vanderbilt University Title: General-relativistic viscous fluids Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon 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 quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon 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 quark-gluon plasma behaves essentially like a relativistic liquid…

• September 22, 2022 10:30 AM
Speaker:
Venue: CMSA Room G10

General Relativity Seminar Speaker: Nikolaos Athanasiou Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell 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…

• September 15, 2022 10:30 AM
Speaker: Professor Pau Figueras
Venue: CMSA Room G10

General Relativity Seminar Title: The Gregory-Laflamme 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 Gregory-Laflamme 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.

• September 08, 2022 10:30 AM
Speaker: Harvey Reall
Venue: CMSA Room G10

General 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

• April 28, 2022 03:35 PM
Speaker: Allen Fang, Sorbonne University
Venue: Virtual

Abstract: The nonlinear stability of the slowly-rotating Kerr-de 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 slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space 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.

• April 21, 2022 10:00 AM
Speaker: Jinhua Wang, Xiamen University
Venue: Virtual

Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (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 Bianchi-Klein-Gordon equations. Moreover, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon 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.

• April 14, 2022 01:00 PM
Speaker: Chao Liu (HUST)
Venue: Virtual

Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.

• March 28, 2022 01:00 PM
Speaker: Emanuele Berti, Johns Hopkins University
Venue: Virtual

Abstract: 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)…

• March 24, 2022 09:30 AM
Speaker: Qian Wang, University of Oxford

Abstract: 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,… • March 21, 2022 01:00 PM Speaker: Prof. Arick Shao (Queen Mary University of London) Title: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes Venue: Virtual Abstract: 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). • March 10, 2022 01:00 PM Speaker: David Fajman (University of Vienna) Title: The Einstein-flow on manifolds of negative curvature Venue: Virtual Abstract: 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. • February 24, 2022 01:00 PM Speaker: Achilleas Porfyriadis Title: Extreme Black Holes: Anabasis and Accidental Symmetry Venue: virtual Speaker: 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. • February 17, 2022 01:00 PM Speaker: Shiraz Minwalla (Tata Institute of Fundamental Research, Mumbai) Title: Black Hole dynamics at Large D Venue: Virtual Abstract: 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. • February 10, 2022 09:30 AM Speaker: Tin Yau Tsang Title: Dihedral ridigity and mass Venue: Virtual 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 discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass). • December 16, 2021 01:00 PM Speaker: Xinliang An, University of Singapore Title: Low regularity ill-posedness for D elastic waves and for D ideal compressible MHD driven by shock formation Venue: Virtual Abstract: 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… • December 02, 2021 01:00 PM Speaker: Professor Geoffrey Compére, Université Libre de Bruxelles Title: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger Venue: Virtual Abstract: 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. • November 19, 2021 01:00 PM Speaker: Nishanth Gudapati, Clark University Title: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U() Symmetric Spacetimes Venue: Virtual Abstract: 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… • November 11, 2021 01:00 PM Speaker: Siyuan Ma, Sorbonne University Title: Sharp decay for Teukolsky equation in Kerr spacetimes Venue: Virtual Abstract: 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.

• November 04, 2021 01:00 PM
Speaker: Elena Giorgi, Columbia University
Venue: Virtual

Abstract: 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.