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.
|Martin Lesourd (BHI)||Title: Shi-Tam’s Existence of Minimal Surfaces from Quasi-Local 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 Schoen-Yau 83 and later Yau 01, which give sufficient conditions for the existence of an apparent horizon within a 3-dimensional initial data set. Shi-Tam 07 have done something analogous in the Riemannian context and obtained the existence of minimal surfaces from conditions on quasi-local 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 quasi-local mass
Abstract: I will describe work in progress with Aghil Alaee and Shing-Tung Yau in which sufficient conditions for the existence of minimal or marginally outer trapped surfaces inside a domain are expressed in terms of the quasi-local mass of the domain.
|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 quasi-local 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 Center-of-Mass at Null Infinity
Abstract: We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion. Our result complements earlier work of Chen-Wang-Yau, where the authors calculate the quasi-local energy and linear momentum at null infinity. Working in the center-of-mass frame, i.e. assuming vanishing of linear momentum at null infinity, we obtain explicit expressions for the angular momentum and center-of-mass at future null infinity in terms of the observables appearing in the Bondi-Sachs expansion of the spacetime metric. This is joint work with Ye-Kai Wang and Shing-Tung Yau.
|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 2-tensors.
|11/8/2019||Pei-Ken 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 on-going joint work with S. Brendle.
|Eric Woolgar (University of Alberta)||
Abstract: Curvature-dimension 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, near-extremal-horizon geometry, and scalar-tensor gravity. I will discuss an application of a Riemannian curvature-dimension bound to horizon topology, and use Lorentzian curvature-dimension 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 self-similar 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 non-rotating 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.
Information about last year’s seminar can be found here.