The Large D Limit of Einstein’s Equations
2021-10-22 09:30 - 10:30 (America/New_York) | MA
Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study, with relatively simple techniques, some of the thorniest problems in black hole physics, such as the non-linear evolution of the instabilities of black strings and black branes, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.

The classical interior of charged black holes with AdS asymptotics
2021-10-28 09:30 - 10:30 | MA
Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. We then consider charged scalars, which are known to condense at low temperatures, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior. The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity. Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on temperature, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures, the final Kasner exponent exhibits fractal-like behavior.

The stability of charged black holes
2021-11-04 13:00 - 14:00 | MA
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.

Sharp decay for Teukolsky equation in Kerr spacetimes
2021-11-11 13:00 - 14:00 | MA
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.

On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes
2021-11-19 13:00 - 14:00 | MA
strong>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 Einstein equations, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.

Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger
2021-12-02 13:00 - 14:00 | MA
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.

Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation
2021-12-16 13:00 - 14:00 | MA
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 for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6times 6$ and $7times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them, we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.

Dihedral ridigity and mass
2022-02-10 09:30 - 10:30 | MA
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).

Black Hole dynamics at Large D
2022-02-17 13:00 - 14:00 | MA
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.

Extreme Black Holes: Anabasis and Accidental Symmetry
2022-02-24 13:00 - 14:00 | 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.

The Einstein-flow on manifolds of negative curvature
2022-03-10 13:00 - 14:00 | MA
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.

Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes
2022-03-21 13:00 - 14:00 | MA
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).

Rough solutions of the $3$-D compressible Euler equations
2022-03-24 09:30 - 10:30 | MA
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 $(v,varrho, omega) in H^stimes H^stimes H^{s’}$, $2<s'<s$. 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 $omegain H^s$, $s>3/2$ and fails for $sle 3/2$, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be $(v,varrho, omega) in H^stimes H^stimes H^{s’}$, $s>2, \, s’>frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves, governed by quasilinear wave equations, and vorticity which is transported by the flow. To overcome this difficulty, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.

Black Hole Spectroscopy
2022-03-28 13:00 - 14:00 | MA
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) What is the current observational status of black hole spectroscopy?

Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4
2022-04-14 09:30 - 10:30 | 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.

Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system
2022-04-21 10:00 - 11:00 | MA
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.

A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
2022-04-28 15:35 - 16:35 | MA
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.

The second law of black hole mechanics in effective field theory
2022-09-08 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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

The Gregory-Laflamme instability of black strings revisited
2022-09-15 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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.

A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
2022-09-22 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.

General-relativistic viscous fluids
2022-09-29 10:30 - 11:30 | 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 with viscosity. More recently, state-of-the-art numerical relativity 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 comprehensive 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.

Duality in Einstein’s Gravity
2022-10-06 10:30 - 23:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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.

Strong Cosmic Censorship
2022-10-13 10:30 - 23:30 | Virtual
General Relativity Seminar

Speaker: Professor Oscar Dias (University of Southampton)

Title: Strong Cosmic Censorship
Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

Love Symmetry of Black Holes
2022-10-20 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Sergei Dubovsky (New York University)

Title: Love Symmetry of Black Holes

Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2,ℝ) symmetry in the suitably defined near zone approximation. We show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2,ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2,ℝ) representations. It is this highest-weight property that forces the static Love numbers to vanish. We show that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. The Love symmetry also exhibits a peculiar UV/IR mixing.

Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity
2022-10-27 10:30 - 11:30 | Virtual
General Relativity Seminar

Speaker: Naqing Xie (Fudan University)
Title: Gravitational Wave, Angular Momentum, and Supertranslation Ambiguity

Abstract: The supertranslation ambiguity of angular momentum is a long-standing and conceptually important issue in general relativity. Recently, there appeared the first definition of angular momentum at null infinity that is supertranslation invariant. However, in the compact binary coalescence community, supertranslation ambiguity is often ignored. We have shown that, in the linearised theory of gravitational wave, the new angular momentum coincides with the classical definition at the quadrupole level. This talk is based on a recent joint work with Xiaokai He and Xiaoning Wu.

Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality
2022-11-03 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar

Speaker: Pengyu Le (BIMSA)
Title: Asymptotic geometry of null hypersurface in Schwarzschild spacetime and null Penrose inequality
Abstract: Null Penrose inequality is an important case of the well-known Penrose inequality on a null hypersurface. It conjectures the relation between the area of the outmost marginally trapped surface and the Bondi mass at null infinity. Following the proposal of Christodoulou and Sauter, we employ the perturbation method to study the asymptotic geometry of null hypersurfaces at null infinity in a perturbed vacuum Schwarzshild spacetime. We explain how to apply this perturbation theory to prove null Penrose inequality on a nearly spherically symmetric null hypersurface in a perturbed vacuum Schwarzschild spacetime.

Schwarzschild-like Topological Solitons in Gravity
2022-11-10 09:30 - 10:30 | Virtual
General Relativity Seminar

Speaker: Pierre Heidmann (Johns Hopkins)
Title: Schwarzschild-like Topological Solitons in Gravity
Abstract: We present large classes of non-extremal solitons in gravity that are asymptotic to four-dimensional Minkowski spacetime plus extra compact dimensions. They correspond to smooth horizonless geometries induced by topology in spacetime and supported by electromagnetic flux, which characterize coherent states of quantum gravity. We discuss a new approach to deal with Einstein-Maxwell equations in more than four dimensions, such that they decompose into a set of Ernst equations. We generate the solitons by applying different techniques associated with the Ernst formalism. We focus on solitons with zero net charge yet supported by flux, and compare them to Schwarzschild black holes. These are also ultra-compact geometries with very high redshift but differ in many aspects. At the end of the talk, we discuss the stability properties of the solitons and their gravitational signatures.

Ringdown and geometry of trapping for black holes
2022-11-17 09:30 - 10:30 | Hybrid
General Relativity Seminar

Speaker: Semyon Dyatlov (MIT)
Title: Ringdown and geometry of trapping for black holes
Abstract: Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild (-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
2022-12-08 09:30 - 10:30 | Virtual
General Relativity Seminar

Speaker: Allen Fang (Princeton)
Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
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 vector field 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.

Testing spacetime geometry with images of supermassive compact objects: Current status and the future
2023-01-26 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: Prashant Kocherlakota (BHI)
Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future
Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.
