CMSA

General Relativity Program
2022-01-24 09:00 - 2022-05-21 17:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses, a conference, and a workshop.
General Relativity Mincourses: March–May, 2022
General Relativity Conference: April 4–8, 2022
General Relativity Workshop: May 2–5, 2022

Program Visitors

Dan Lee, CMSA/CUNY, 1/24/22 – 5/20/22
Stefan Czimek, Brown, 2/27/22 – 3/3/22
Lan-Hsuan Huang, University of Connecticut, 3/13/22 – 3/19/222, 3/21/22 – 3/25/22, 4/17 /22– 4/23/22
Mu-Tao Wang, Columbia, 3/21/22 – 3/25/22, 5/7/22 – 5/9/22
Po-Ning Chen, University of California, Riverside, 3/21/22 – 3/25/22, 5/7/22–5/9/22
Marnie Smith, Imperial College London, 3/27/22 – 4/11/22
Christopher Stith, University of Michigan, 3/27/22 – 4/23/22
Martin Taylor, Imperial College London, 3/27/22 – 4/11/22
Marcelo Disconzi, Vanderbilt, 5/9/22 – 5/21/22
Lydia Bieri, University of Michigan, 5/5/22 – 5/9/22

General Relativity Program Minicourses
2022-03-01 10:00 - 2022-05-17 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Minicourses
General Relativity Program Minicourses

During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.

Schedule
Speaker
Title
Abstract

March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
Dr. Stefan Czimek
Characteristic Gluing for the Einstein Equations
Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).

March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.
Prof. Lan-Hsuan Huang
Existence of Static Metrics with Prescribed Bartnik Boundary Data
Abstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is
1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regular
Video on Youtube: March 22, 2022

March 29 – April 1, 2022 10:00am – 12:00pm ET, each day
Location: Hybrid. CMSA main seminar room, G-10.
Prof. Martin Taylor
The nonlinear stability of the Schwarzschild family of black holes
Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.

April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom only
Prof. Håkan Andréasson
Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.
Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.
Video 4/19/2022
Video 4/22/2022

May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
Prof. Marcelo Disconzi
A brief overview of recent developments in relativistic fluids
Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.
1. Set-up, review of standard results, physical motivation.
2. The relativistic Euler equations: null structures and the problem of shocks.
3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
4. Relativistic viscous fluids.
Video 5/16/2022
Video 5/17/2022

General Relativity Conference
2022-04-04 09:30 - 2022-04-08 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Schedule | April 4–8, 2022
Monday, April 4, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Pieter Blue, University of Edinburgh, UK
(virtual)
Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge
Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of the Einstein equation in this gauge, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975, Chrzanowski introduced the “outgoing radiation gauge”, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently, using a flow along null geodesics, we have constructed a new gauge such that, in this gauge, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge.
This is joint work with Lars Andersson, Thomas Backdahl, and Siyuan Ma.

10:30 am–11:30 am
Peter Hintz, ETH Zürich
(virtual)
Title: Mode stability and shallow quasinormal modes of Kerr-de Sitter
black holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe, such as our own, with cosmological constant $Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question), mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $sigma$ in any fixed half space $Imsigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $mto 0$ in which, depending on the scaling, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.

11:30 am–12:30 pm
Lars Andersson, Albert Einstein Institute, Germany
(virtual)
Title: Gravitational instantons and special geometry
Abstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk, I will introduce some notions of special geometry, discuss known examples, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $mathrm{CP}^2 setminus mathrm{S}^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner, cf. https://arxiv.org/abs/2112.11863.

12:30 pm–1:30 pm
break

1:30 pm–2:30 pm
Martin Taylor, Imperial College London
(virtual)
Title: The nonlinear stability of the Schwarzschild family of black holes
Abstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

2:30 pm–3:30 pm
Po-Ning Chen, University of California, Riverside
(virtual)
Title: Angular momentum in general relativity

Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960s, due to the ‘supertranslation ambiguity’. In this talk, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller, Mu-Tao Wang, Ye-Kai Wang, and Shing-Tung Yau.

3:30 pm–4:00 pm
break

4:00 pm–5:00 pm
Dan Lee, Queens College (CUNY)
(hybrid: in person & virtual)
Title: Stability of the positive mass theorem
Abstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem, focusing on recent work with Kazaras and Khuri, in which we proved that if one assumes a lower Ricci curvature bound, then stability holds with respect to pointed Gromov-Hausdorff convergence.

Tuesday, April 5, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Xinliang An, National University of Singapore
(virtual)
Title: Anisotropic dynamical horizons arising in gravitational collapse
Abstract: Black holes are predicted by Einstein’s theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk, we will present several results in these directions. First, in a joint work with Qing Han, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second, in joint works with Dejan Gajic and Ruixiang Zhang, for the spherically symmetric Einstein-scalar field system, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism. If time permits, some results on fluid dynamics will also be addressed.

10:30 am–11:30 am
Sergiu Klainerman, Princeton
(virtual)
Title: Nonlinear stability of slowly rotating Kerr solutions
Abstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.

11:30 am–12:30 pm
Siyuan Ma, Sorbonne University
(virtual)
Title: Sharp decay for Teukolsky master equation
Abstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Jonathan Luk, Stanford
(virtual)
Title: A tale of two tails
Abstract: Motivated by the strong cosmic censorship conjecture, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).

2:30 pm–3:30 pm
Gary Horowitz, University of California Santa Barbara
(virtual)
Title: A new type of extremal black hole
Abstract: I describe a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero, if quantum matter is added, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Lydia Bieri, University of Michigan
(virtual)
Title: Gravitational radiation in general spacetimes
Abstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

Wednesday, April 6, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Gerhard Huisken, Mathematisches Forschungsinstitut Oberwolfach
(virtual)
Title: Space-time versions of inverse mean curvature flow
Abstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.

10:30 am–11:30 am
Carla Cederbaum, Universität Tübingen, Germany
(virtual)
Title: Coordinates are messy
Abstract: Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M,g,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.

11:30 am–12:30 pm
Stefanos Aretakis, University of Toronto
(virtual)
Title: Observational signatures for extremal black holes
Abstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Jared Speck, Vanderbilt University
(virtual)
Title: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow
Abstract: In the last two decades, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia, M. Disconzi, and J. Luk.

2:30 pm–3:30 pm
Lan-Hsuan Huang, University of Connecticut
(virtual)
Title: Null perfect fluids, improvability of dominant energy scalar, and Bartnik mass minimizers
Abstract: We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture.
Along the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Demetre Kazaras, Duke University
(virtual)
Title: Comparison geometry for scalar curvature and spacetime harmonic functions
Abstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

Thursday, April 7, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Piotr Chrusciel, Universitat Wien
(virtual)
Title: Maskit gluing and hyperbolic mass
Abstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.

10:30 am–11:30 am
Greg Galloway, University of Miami (virtual)
Title: Initial data rigidity and applications
Abstract: We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP, 2021), and look at some consequences. In a note with Piotr Chruściel (CQG 2021), we showed how to use this result, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result, to obtain a hyperbolic PMT result with boundary. This will also be discussed.

11:30 am–12:30 pm
Pengzi Miao, University of Miami
(virtual)
Title: Some remarks on mass and quasi-local mass
Abstract: In the first part of this talk, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello, and with H.C. Jang.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Yakov Shlapentokh Rothman, Princeton
(hybrid: in person & virtual)
Title: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations
Abstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.

2:30 pm–3:30 pm
Marcelo Disconzi, Vanderbilt University
(virtual)
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 with viscosity. More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Maxime van de Moortel, Princeton
(hybrid: in person & virtual)
Title: Black holes: the inside story of gravitational collapse
Abstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models, the global structure of the black hole interior has largely remained unexplored.
These questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.
I will present my recent resolution of these problems in spherical gravitational collapse, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.

Friday, April 8, 2022

Time (ET)
Speaker
Title/Abstract

9:30 am–10:30 am
Ye-Kai Wang, National Cheng Kun University, Taiwan
(virtual)
Title: Supertranslation invariance of angular momentum at null infinity in double null gauge
Abstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing
how Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen, Jordan Keller, Mu-Tao Wang, and Shing-Tung Yau.

10:30 am–11:30 am
Zoe Wyatt, King’s College London
(virtual)
Title: Global Stability of Spacetimes with Supersymmetric Compactifications
Abstract: Spacetimes with compact directions which have special holonomy, such as Calabi-Yau spaces, play an important role in
supergravity and string theory. In this talk I will discuss a recent work with Lars Andersson, Pieter Blue and Shing-Tung Yau, where we show the global, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.

11:30 am–12:30 pm
Elena Giorgi, Columbia University
(hybrid: in person & virtual)
Title: The stability of charged black holes
Abstract: Black hole 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.

12:30 pm–1:30 pm
Break

1:30 pm–2:30 pm
Marcus Khuri, Stony Brook University
(virtual)
Title: The mass-angular momentum inequality for multiple black holes

Abstract: Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected, axisymmetric, maximal, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain, Chrusciel-Li-Weinstein, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from
R^3 Gamma –>H^2 where Gamma is a coordinate axis. This is joint work with Q. Han, G. Weinstein, and J. Xiong.

2:30 pm–3:30 pm
Martin Lesourd, Harvard
(hybrid: in person & virtual)
Title: A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature
Abstract: I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau, Prof. D. A. Lee, and R. Unger.

3:30 pm–4:00 pm
Break

4:00 pm–5:00 pm
Georgios Moschidis, Princeton
(virtual)
Title: Weak turbulence for the Einstein–scalar field system.
Abstract: In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity, lead to the formation of black holes after sufficiently long time.
In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time, as well as estimating the decoherence rate of those beams.
