Testing GR with GWs
2023-05-04 09:30 - 10:30 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Vitor Cardoso, IST, Lisbon and The Niels Bohr Institute, Copenhagen
Title: Testing GR with GWs
Abstract: One of the most remarkable possibilities of General Relativity concerns gravitational collapse to black holes, leaving behind a geometry with light rings, ergoregions and horizons. These peculiarities are responsible for uniqueness properties and energy extraction mechanisms that turn black holes into ideal laboratories of strong gravity, of particle physics (yes!) and of possible quantum-gravity effects. I will discuss some of the latest progress in tests of General Relativity with black holes.

Positivity of Static quasi-local Mass in general relativity
2023-05-11 13:30 - 14:30 | Virtual
General Relativity Seminar
Speaker: Aghil Alaee, Clark University
Title: Positivity of Static quasi-local Mass in general relativity
Abstract: In this talk, we review results on the PMT of quasi-local masses and prove the positivity of static quasi-local masses with respect to the AdS and AdS Schwarzschild spacetimes.

Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole
2023-07-05 14:00 - 15:00 | Jefferson 453, 17 Oxford St, Cambridge, MA 02138, MA
General Relativity Seminar
Speaker: Suman Kundu (Weizmann Institute)
Title: ‘Grey Galaxy’ as the endpoint of the Kerr-AdS super radiant blackhole
Abstract: Kerr AdS$_{d+1}$ black holes for $dgeq 3$ suffer from classical superradiant instabilities over a range of masses near extremality. We conjecture that these instabilities settle down into Grey Galaxies (GG)s – a new class of solutions to Einstein’s equations which we construct for $d=3$. Grey Galaxies consist of an $omega=1$ black hole in the `centre’ of $AdS$, surrounded by a uniformly thick and very large disk of thermal bulk matter that revolves around the centre of AdS at the speed of light. The parametrically low energy density and parametrically large radius of the gas disk are inversely related; as a consequence, the gas carries a finite fraction of the total energy. Grey Galaxy saddles exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr AdS black holes and the gas. In addition to a smooth piece, the boundary stress tensor of these solutions includes a contribution from a delta function localized at the `equator’ of the boundary sphere, a term which may be used as an order parameter that sharply distinguishes GG solutions from ordinary Kerr-Black hole saddles. We also construct `Revolving Black Hole (RBH) saddles’, macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, that describe black holes revolving around the centre of $AdS$, at the fixed radial location but in a quantum wave function in the angular directions. RBH saddles turn out to be (marginally) entropically subdominant to GG saddles. We argue that supersymmetric versions of RBH saddles exist and have interesting consequences for the spectrum of SUSY states in, e.g. ${cal N}=4$ Yang-Mills theory.

Pole skipping, quasinormal modes, shockwaves and their connection to chaos
2023-09-12 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Diandian Wang(Harvard University)
Title: Pole skipping, quasinormal modes, shockwaves and their connection to chaos
Abstract: A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving pole-skipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higher-derivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.

Quantization of causal diamonds in 2+1 dimensional gravity
2023-09-19 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Rodrigo Silva, University of Maryland
Title: Quantization of causal diamonds in 2+1 dimensional gravity
Abstract: We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

Geometry at Strong coupling for amplitudes/Wilson loops
2023-09-26 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Lionel Mason (Oxford)
Title: Geometry at Strong coupling for amplitudes/Wilson loops
Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

A Smooth Horizon without a Smooth Horizon
2023-10-03 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Chethan Krishnan (IISc Bangalore)
Title: A Smooth Horizon without a Smooth Horizon
Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

Tidal Squeezing of Black Holes
2023-10-10 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Maria Rodriguez (Utah)
Title: Tidal Squeezing of Black Holes
Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

Resolving memory in numerical relativity, and fixing BMS frames for modeling
2023-10-24 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Leo Stein (Mississippi)
Title: Resolving memory in numerical relativity, and fixing BMS frames for modeling
Abstract: Numerical relativity waveforms serve as ground truth for detection and parameter estimation of binary black hole mergers. Most NR waveforms to date miss memory effects, as they were extracted from simulations using an approximation called extrapolation. I will report on the SXS collaboration’s capacity to resolve memory effects in production NR simulations using Cauchy-characteristic evolution (CCE), and in the future with Cauchy-characteristic matching (CCM). I will further report on how BH perturbation and post-Newtonian theory furnish natural BMS frames. With these BMS frames, we can extract well-defined remnant quantities, perform precision ringdown modeling, and build complete surrogate waveform models that capture memory effects.

Fluid stabilization in slowly expanding cosmological spacetime
2023-11-07 11:00 - 12:00 | Hybrid – G10
General Relativity Seminar
Speaker: David Fajman (Vienna)
Title: Fluid stabilization in slowly expanding cosmological spacetime
Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.

Talk via Zoom, broadcast in G10

Quasi-Local Mass in a Binary Black Hole Merger
2023-11-14 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Daniel Kolb (Max Planck Institute)
Title: Quasi-Local Mass in a Binary Black Hole Merger
Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and Yau in 2009. A closed 2-surface bounding the region of interest is embedded isometrically into Minkowski space. The mass is then calculated by comparing the extrinsic geometries. The Wang-Yau mass has many desirable properties, but it has previously not been calculated for surfaces in dynamical spacetimes. To remedy this, we will discuss how the Wang-Yau mass can be computed in practice and extend the definition to surfaces important in black hole dynamics: their quasi-local horizons. Finally, we look at how this mass behaves in a merger of black holes.

Remarkable symmetries of rotating black holes
2023-11-28 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: David Kubiznak (Charles University)
Title: Remarkable symmetries of rotating black holes
Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its ‘square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.

The Feynman propagator and self-adjointness
2023-12-05 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Andras Vasy (Stanford)
Title: The Feynman propagator and self-adjointness
Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow.

A quasi-local mass in general relativity
2024-01-30 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Aghil Alaee, Clark University
Title: A quasi-local mass in general relativity
Abstract: In this talk, we define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime. In contrast to other quasi-local masses, this new quasi-local mass/energy has a quasi-local proof of positivity. This positivity property is for spacelike surfaces with any topology. Moreover, we show that it has desired asymptotic behaviors at null and spatial infinity of asymptotically flat spacetimes. Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau.

Noncompact n-dimensional Einstein spaces as attractors for the Einstein flow
2024-02-06 10:00 - 11:00 | Virtual
General Relativity Seminar
Speaker: Jinhua Wang, Xiamen University
Title: Noncompact n-dimensional Einstein spaces as attractors for the Einstein flow
Abstract: We prove that along with the Einstein flow, any small perturbations of an $n$($ngeq4$)-dimensional, non-compact negative Einstein space with some “non-positive Weyl tensor” lead to a unique and global solution, and the solution will be attracted to a noncompact Einstein space that is close to the background one. The $n=3$ case has been addressed by Wang-Yuan, while in dimension $ngeq 4$, as we know, negative Einstein metrics in general have non-trivial moduli spaces. This fact is reflected on the structure of Einstein equations, which further indicates no decay for the spatial Weyl tensor. Furthermore, it is suggested in the proof that the mechanic preventing the metric from flowing back to the original Einstein metric lies in the non-decaying character of spatial Weyl tensor. In contrary to the compact case considered in Andersson-Moncrief, our proof is independent of the theory of infinitesimal Einstein deformations. Instead, we take advantage of the inherent geometric structures of Einstein equations and develop an approach of energy estimates for a hyperbolic system of Maxwell type.
References – arXiv: 2209.15244, 2309.15152, 2311.00868

Characteristic Initial Value Problem for the 3D Compressible Euler Equations
2024-02-13 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Sifan Yu, NUS
Title: Characteristic Initial Value Problem for the 3D Compressible Euler Equations
Abstract: We present the first result for the characteristic initial value problem of the compressible Euler equations in three space dimensions without any symmetry assumption. We allow presence of vorticity and consider any equation of state. Compared to the standard Cauchy problem, where initial data can be freely prescribed on a constant-time hypersurface, we formulate the problem by distinguishing between the “free-component” and the “constrained-component” of the initial data. The latter is to be solved by the “free-component” utilizing the properties of the compressible Euler equations on the initial null hypersurfaces. Then, we establish a priori estimates, followed by a local well-posedness and a continuation criterion argument. Moreover, we prove a regularity theory in Sobolev norms. Our analysis critically relies on the vectorfield method due to the nature of the problem. This is a joint work with Jared Speck.

Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
2024-02-20 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: He Mei, Shenzhen University
Title: Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
Abstract: In this talk, I will present a work on the long time dynamics of solutions to the defocusing semilinear wave equations on the Schwarzschild black hole spacetimes. For sufficiently smooth and localized initial data, we show that the solution decays in the domain of outer communication. The proof relies on a vector field method of Dafermos-Rodnianski together with Strichartz estimates for linear waves by Marzuola-Metcalfe-Tataru-Tohaneanu.

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
2024-02-27 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Nishanth Gudapati, Clark University
Title: On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
Abstract: The Kerr black hole stability problem is an important open problem in general relativity. In this talk, I will focus on the role of energy methods in the axisymmetric stability of Kerr black hole spacetimes. In particular, I will discuss the construction and the application of a positive Hamiltonian energy for axially symmetric Maxwell and Einstein perturbations of sub-extremal Kerr black hole spacetimes.

High order WENO finite difference scheme for Einstein-Yang-Mills equations
2024-03-05 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Yuewen Chen, Tsinghua University
Title: High order WENO finite difference scheme for Einstein-Yang-Mills equations
Abstract: In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.

Scattering Rigidity Problem
2024-03-19 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Jin Jia, Hunan University
Title: Scattering Rigidity Problem
Abstract: If the asymptotic behavior of a solution to a nonlinear equation is the same as that of a solution to its linearized equation, it is called a scattering solution. Scattering phenomena are widely observed near steady-state solutions of various mathematical physics equations, such as water wave equations, Einstein equations, MHD equations, and Vlasov-Poisson equations. This report takes these equations as examples to provide the definition of scattering operator and its relation to radiation fields. It explains the concepts of scattering rigidity problem and scattering completeness problem, and introduces the latest discoveries of the speaker in the general solution approach to scattering rigidity problem.

Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields
2024-04-02 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Zihan Yan, Cambridge University

Title: Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields

Abstract: Expanding the work of arXiv:1504.08040, we show that black holes obey a second law for linear perturbations to bifurcate Killing horizons, in any covariant higher curvature gravity coupled to scalar and vector fields. The vector fields do not need to be gauged, and (like the scalars) can have arbitrary non-minimal couplings to the metric. The increasing entropy has a natural expression in covariant phase space language, which makes it manifestly invariant under JKM ambiguities. An explicit entropy formula is given for f(Riemann) gravity coupled to vectors, where at most one derivative acts on each vector. Besides the previously known curvature terms, there are three extra terms involving differentiating the Lagrangian by the symmetric vector derivative (which therefore vanish for gauge fields).

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
2024-04-16 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Xiaoyi Liu, UCSB
Title: New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
Abstract: We consider four-dimensional Euclidean gravity in a finite cavity. We point out that there exists a one-parameter family of boundary conditions, parameterized by a real constant, where a suitably Weyl-rescaled boundary metric is fixed, and all give a well-posed elliptic system, as opposed to the Dirichlet boundary condition. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution and have similar thermodynamics to the Dirichlet case. We study the stability behavior of several geometries under these boundary conditions in both Euclidean and Lorentzian signatures and find two puzzles.

Quantum Energy Inequalities
2024-04-23 10:00 - 11:00 | Virtual
General Relativity Seminar
Speaker: Chris Fewster, York University
Title: Quantum Energy Inequalities
Abstract: Many theorems of mathematical relativity, including singularity and positive mass theorems, include the classical energy conditions among their hypotheses. However, matter described by quantum field theory can violate the classical energy conditions and indeed there is no lower bound to the energy density at a given point as the quantum state is varied. Do the classical theorems apply to quantised matter?
In this talk I discuss Quantum Energy Inequalities, lower bounds on averages of the energy density along timelike curves or over spacetime regions, that have been proved in QFT and are the remnants of the classical energy conditions after quantisation. I will also discuss some of their consequences.

Real-time observables in horizon thermodynamics
2024-05-07 14:00 - 15:00 | Virtual
General Relativity Seminar
Speaker: Albert Law, Stanford
Title: Real-time observables in horizon thermodynamics
Abstract: Euclidean black hole 1-loop determinants have recently been shown to compute a renormalized thermal canonical partition function for free fields in Lorentzian signature. A key ingredient is a ‘quasinormal mode (QNM) character’, whose Fourier transform equals the renormalized spectral density of the single-particle Hamiltonian. Using a static patch in de Sitter space as an example, in this talk, I will offer new perspectives on the QNM character, including its connection with the local density of states for the single-particle quantum mechanical problem associated with the Klein-Gordon equation, and its direct relationships with (thermal) correlators of the free fields. I will discuss how these considerations might point toward a generalization to interacting theories.

An analogue of non-interacting quantum field theory in Riemannian signature
2024-05-13 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Mikhail Molodyk, Stanford
Title: An analogue of non-interacting quantum field theory in Riemannian signature
Abstract: Recent advances using microlocal tools have led to constructions, for wave operators on various classes of spacetimes, of four distinguished Fredholm inverses which have the singular behavior required of retarded, advanced, Feynman, and anti-Feynman propagators in QFT. Vasy and Wrochna have used these to define a QFT on asymptotically Minkowski spacetimes, for which they construct Hadamard states described by asymptotic data at infinity. I will describe an analogue of this construction on Riemannian manifolds with two asymptotically conic ends, defining quantum fields satisfying the Helmholtz equation and using scattering data to construct states satisfying a wavefront mapping-property version of the Hadamard condition. The absence of a spacetime interpretation lends itself to a sharper focus on the theory’s analytic structure, from whose perspective the Feynman propagators are no less natural than the advanced/retarded ones. I will also highlight some differences between Feynman propagators defined as distinguished inverses and as time-ordered expectations. Based on joint work with András Vasy.

Compactified Hyperboloidal Evolution in Numerical Relativity
2024-08-15 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Shalabh Gautam, International Center for Theoretical Sciences, Tata Institute of Fundamental Research
Title: Compactified Hyperboloidal Evolution in Numerical Relativity
Abstract: In the field of numerical relativity, a major challenge is to incorporate future null infinity into the computational domain using a well-posed formulation. Achieving this goal would not only allow us to accurately simulate any astrophysical system, such as binary black holes, and extract the resulting signal, like gravitational waves, at future null infinity, but it would also facilitate the study of various fundamental phenomena. One proposed solution is to use hyperboloidal slices. In this presentation, I will introduce an alternative approach to numerical relativity that leverages these slices in spherical symmetry. I will also discuss our ongoing efforts to establish a well-posed formulation of the Einstein Field Equations on these slices, and propose numerical schemes to ensure stability and convergence for linear hyperbolic systems over long durations. Additionally, I will present our method for constructing initial data corresponding to an asymptotically flat spacetime. A natural extension of our work will be to generalize these methods to the Einstein Field Equations with appropriate initial data in the full 3d.

New Energy Inequality in AdS
2024-09-24 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Diandian Wang, Harvard University
Title: New Energy Inequality in AdS
Abstract: I will describe evidence for a new energy inequality in asymptotically AdS spacetimes whose conformal boundary contains a spatial circle. It is in some sense analogous but crucially different to the Penrose inequality. In the AdS4 case, this generalizes the Horowitz-Myers conjecture. I will show how static solutions play an interesting role in determining the shape of the function that bounds the gravitational energy.

Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
2024-10-01 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Daniel Kapec, Harvard
Title: Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
Abstract: Recent work on the quantum mechanics of near-extremal non-supersymmetric black holes has identified a characteristic scaling of the low temperature black hole partition function. This result has only been derived using the path integral in the near-horizon region and relies on many assumptions. We discuss how to derive the scaling for the near-extremal rotating BTZ black hole from a calculation in the full black hole background using the Denef-Hartnoll-Sachdev (DHS) formula, which expresses the 1-loop determinant of a thermal geometry in terms of a product over the quasinormal mode spectrum. We also derive the spectral measure for fields of any spin in Euclidean BTZ and use it to provide a new proof of the DHS formula and a new, direct derivation of the BTZ heat kernel. The computations suggest a path to proving the scaling for the asymptotically flat 4d Kerr black hole.

Continuation of solutions of Einstein's equations
2024-10-08 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Oswaldo Vazquez, Northeastern University
Title: Continuation of solutions of Einstein’s equations
Abstract: Klainerman-Rodnianski improved the continuation criterion for the solutions of Einstein’s equations proved by Michael Anderson using Kirchoff-Sobolev type parametrix and geometric Littlewood-Paley theory. Using their technique but a new parametrix we prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative criteria under which the physical spacetime can be extended indefinitely in the future as a solution to the Cauchy problem of the Einstein equations given regular initial data. In particular, we show that a gauge-invariant H^2 Sobolev norm of the spacetime Riemann curvature remains bounded in the future time direction provided the so-called deformation tensor of the unit timelike vector field normal to the chosen CMC hypersurfaces verifies a spacetime L^{infty} bound.

Gravitational collapse to extremal Reissner-Nordström and the third law of black hole thermodynamics
2024-10-15 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Christoph Kehle, MIT
Title: Gravitational collapse to extremal Reissner-Nordström and the third law of black hole thermodynamics
Abstract: In this talk, I will present a proof that extremal Reissner-Nordström black holes can form in finite time in gravitational collapse of charged matter. In particular, this construction provides a definitive disproof of the “third law” of black hole thermodynamics. I will also discuss recent works showing that extremal black holes take on a central role in gravitational collapse, giving rise to a new conjectural picture of “extremal critical collapse.” This is joint work with Ryan Unger (Stanford).
