During the Fall 2019 Semester, a weekly seminar will be held on General Relativity. The seminar will take place at on Fridays at 10:30am virtually. Please email the seminar organizers to obtain a link.
The schedule will be updated below.
|2/7/2020||Lan-Hsuan Huang (University of Connecticut)||Title: Improvability of the dominant energy scalar and Bartnik’s stationary conjecture
Abstract: In this talk, we will introduce the concept of improvabilty of the dominant energy scalar and discuss strong consequences of non-improvability. We employ new, large families of deformations of the modified Einstein constraint operator and show that, generically, their adjoint linearizations are either injective, or else one can prove that kernel elements satisfy a “null-vector equation”. Combined with a conformal argument, we make significant progress toward Bartnik’s stationary conjecture. More specifically, we prove that a Bartnik minimizing initial data set can be developed into a spacetime that both satisfies the dominant energy condition and carries a global Killing field. We also show that this spacetime is vacuum near spatial infinity. This talk is based on the joint work with Dan Lee.
|2/14/2020||Yuewen Chen (CMSA)||Title: Solutions of Jang’s Equation Inside Black Holes
Abstract: Jang’s equation is a degenerate elliptic differential equation which plays an important role in the positive mass theorem. In this talk, we describe a high order WENO (Weighted Essentially Non-Oscillatory) scheme for the Jang’s equation. Some special solutions will be shown, such as those possessing spherical symmetry and axial symmetry.
|Alex Lupsasca (Harvard)||Title: The Kerr 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 itself composed of an infinite sequence of self-similar subrings. Each subring is a lensed image of the main emission, indexed by the number of photon orbits executed around the black hole. I will review recent theoretical advances in our understanding of lensing by Kerr black holes, based on arXiv:1907.04329, 1910.12873, and 1910.12881. In particular, I will describe the critical parameters γ, δ, and τ that respectively control the demagnification, rotation, and time delay of successive lensed images of a source. These observable parameters encode universal effects of general relativity, which are independent of the details of the emitting matter and also produce strong, 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 such as a future extension of the EHT to space.
|2/28/2020||Po-Ning Chen (University of California, Riverside)||Title: A quasilocal charged Penrose inequality
Abstract: In this talk, we will discuss a quasi-local Penrose inequality with charges for time-symmetric initial data of the Einstein-Maxwell equation. Namely, we derive a lower bound for Brown-York type quasi-local mass in terms of the horizon area and the electric charge. The inequality we obtained is sharp in the sense that equality holds for surfaces in the Reissner-Nordström manifold. This talk is based on joint work with Stephen McCormick.
|Nikolaos Athanasiou (University of Oxford)||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 recent result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.
|3/13/2020||Hsin-Yu Chen (BHI)||This meeting will be taking place virtually on Zoom.|
|3/27/2020||Sven Hirsch (Duke University)||This meeting will be taking place virtually on Zoom.
Abstract: The purpose of this talk is twofold: First we present a new proof of the spacetime positive mass theorem (joint with Demetre Kazaras and Marcus Khuri); second we discuss some new results about the topology of initial data sets (joint with Martin Lesourd).
The spacetime positive mass theorem that the mass of an initial data set is non-negative with equality if and only if the initial data set arises as subset of Minkowski space. This result has first been proven by Schoen and Yau using Jang’s equation. There are further proofs by Witten using spinors and by Eichmair, Huang, Lee and Schoen using MOTS. Our proof uses Stern’s integral formula technique and also leads to a new explicit lower bound of the mass which is even valid when the dominant energy condition is not satisfied.
A central conjecture in mathematical relativity is the final state conjecture which states that initial data sets will eventually approach Kerr black holes. In particular, this would imply that the space of initial data sets is path connected. Building upon the work of Marques and using deep and beautiful results of Carlotto and Li, we show that indeed the space of initial data set with compact trapped interior boundary is path connected.
|4/3/2020||Hyun Chul Jang (University of Connecticut)||This meeting will be taking place virtually on Zoom.Title: Mass rigidity of asymptotically hyperbolic spaces and some splitting theorems
Abstract: In this talk, we will discuss the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. That is, if the mass equality holds, then the manifold is isometric to hyperbolic space. The proof used a variational approach with the scalar curvature constraint. It also involves an investigation on a type of Obata’s equations, which leads to recent splitting results with Galloway. This talk is based on the joint works with L.-H. Huang and D. Martin, and with G. J. Galloway.
|4/10/2020||Chao Li (Princeton)||This meeting will be taking place virtually on Zoom.|
|4/17/2020||Brian Allen (University of Hartford)||This meeting will be taking place virtually on Zoom.|
|4/24/2020||Daniel Stern (University of Toronto)||This meeting will be taking place virtually on Zoom.|
|5/8/2020||Anna Sakovich (Uppsala University)|
Information about last year’s seminar can be found here.