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.
|10/25/2019||Christina Sormani (CUNY)||Title: Scalar Curvature and Intrinsic Flat Convergence
Abstract: After reviewing the definition of intrinsic flat convergence, I will present open problems on the almost rigidity or stability of classic rigidity theorems for manifolds with scalar curvature bounds and survey partial results towards these conjectures.
|11/1/2019||Peter Hintz (MIT)||TBA|
|11/8/2019||Pei-Ken Hung (MIT)||TBA|
|11/15/2019||Eric Woolgar (University of Alberta)||TBA|
|11/22/2019||Sahar Hadar (BHI)||TBA|
Information about last year’s seminar can be found here.