During the Fall 2019 Semester, a weekly seminar will be held on General Relativity. The seminar will take place at on Friday’s at 10:30am in Science Center 530.
The schedule will be updated below.
Date  Speaker  Title/Abstract 

9/13/2019
CMSA G02 
Martin Lesourd (BHI)  Title: ShiTam’s Existence of Minimal Surfaces from QuasiLocal Mass
Abstract: Thorne’s hoop conjecture is an intuitive hypothesis intended to capture necessary and sufficient conditions for the existence of a black hole region. The first result in this direction was SchoenYau 83 and later Yau 01, which give sufficient conditions for the existence of an apparent horizon within a 3dimensional initial data set. ShiTam 07 have done something analogous in the Riemannian context and obtained the existence of minimal surfaces from conditions on quasilocal mass. We shall review the main ideas of their proof. 
9/20/2019  Martin Lesourd (BHI)  Title: Existence of minimal or marginally outer trapped surfaces from quasilocal mass
Abstract: I will describe work in progress with Aghil Alaee and ShingTung Yau in which sufficient conditions for the existence of minimal or marginally outer trapped surfaces inside a domain are expressed in terms of the quasilocal mass of the domain. 
10/4/2019  Cancelled  
10/11/2019  Graham Cox (Memorial University)  Title: Blowup solutions of Jang’s equation near a spacetime singularity
Abstract: Jang’s equation is a semilinear elliptic equation define on an initial data set. It was shown by Schoen and Yau that the (non)existence of global solutions is closely related to the existence of marginally outer trapped surfaces (MOTS), which are quasilocal analogues of black hole boundaries. As a result, Jang’s equation can be used to prove the existence of MOTS by imposing appropriate geometric conditions on the initial data set. These proofs proceed by contradiction: one assumes there is a global solution, then proves that its existence is not compatible with the given geometric assumptions. In this talk I will outline a constructive approach to proving the existence of MOTS. In particular, I will consider a distinguished family of spacelike hypersurfaces in the maximally extended Schwarzschild spacetime, and prove that Jang’s equation admits no global solutions once the hypersurfaces become sufficiently close to the r=0 singularity. This suggests a general strategy for relating spacetime singularities to the presence of MOTS. This is joint with Amir Aazami. 
10/18/2019  Jordan Keller (BHI)  Title: Angular Momentum and CenterofMass at Null Infinity
Abstract: We calculate the limits of the quasilocal angular momentum and centerofmass defined by ChenWangYau for a family of spacelike twospheres approaching future null infinity in an asymptotically flat spacetime admitting a BondiSachs expansion. Our result complements earlier work of ChenWangYau, where the authors calculate the quasilocal energy and linear momentum at null infinity. Working in the centerofmass frame, i.e. assuming vanishing of linear momentum at null infinity, we obtain explicit expressions for the angular momentum and centerofmass at future null infinity in terms of the observables appearing in the BondiSachs expansion of the spacetime metric. This is joint work with YeKai Wang and ShingTung Yau. 
10/25/2019  Cancelled  
11/1/2019  Peter Hintz (MIT)  Title: Linear stability of slowly rotating Kerr black holes
Abstract: I will describe joint work with Dietrich Häfner and András Vasy in which we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild and slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. Our proof uses a detailed description of the low energy resolvent of an associated wave equation on symmetric 2tensors. 
11/8/2019  PeiKen Hung (MIT) 
Abstract: In this talk, I will discuss a wave equation for one forms in the Schwarzschild spacetime which is the linearization of a modified wave map gauge. The equation behaves like a damped wave equation and we obtain robust estimates. In particular, it allows us to show the stability of the modified wave map equation. This is ongoing joint work with S. Brendle.

11/13/2019
Wednesday 1:00pm CMSA G10 
Eric Woolgar (University of Alberta) 
Abstract: Curvaturedimension inequalities are modifications of a Ricci curvature bound or, in the language of relativity, an energy condition. They have proved useful in applications of Fourier analysis to diffusion processes. As tools to prove theorems in Riemannian geometry and general relativity, they are often as powerful as the usual Ricci curvature bounds and can yield new results. Applications include static Einstein metrics, nearextremalhorizon geometry, and scalartensor gravity. I will discuss an application of a Riemannian curvaturedimension bound to horizon topology, and use Lorentzian curvaturedimension bounds to prove some singularity theorems and splitting theorems. Parts of the talk are based on joint work with Marcus Khuri, Will Wylie, and Greg Galloway.

11/22/2019  Sahar Hadar (BHI)  Title: Universal signatures of a black hole’s photon ring
Abstract: The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin “photon ring,” which is composed of an infinite sequence of selfsimilar subrings that are indexed by the number of photon orbits around the black hole. The subrings approach the edge of the black hole “shadow,” becoming exponentially narrower but weaker with increasing orbit number, with seemingly negligible contributions from high order subrings. In the talk, I will discuss the structure of the photon ring, starting with nonrotating black holes, and then proceeding to the complex patterns that emerge when rotation is taken into account. Subsequently I will argue that the subrings produce strong and universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array. 
11/29/2019  Thanksgiving Holiday  
12/6/2019  
12/13/2019 
Information about last year’s seminar can be found here.