Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)
A Rigidity Theorem for Asymptotically Flat Static Manifolds and its Applications
Brian Harvie (NCTS)
Abstract
In general relativity, many physically and mathematically important questions concern the uniqueness of the Schwarzschild space. For example, Israel's black hole uniqueness theorem states that the Schwarzschild space is the only asymptotically flat static manifold with stable minimal boundary, and similar uniqueness questions for photon surfaces and for static metric extensions have recently generated great interest.
In this talk, I will present a new approach to these questions that is based on a recently-discovered Minkowski inequality for asymptotically flat static manifolds. We prove for that the equality is achieved only on coordinate spheres in the Schwarzschild space under natural boundary assumptions. We derive several new uniqueness theorems for Schwarzschild using this rigidity. Notably, we establish global uniqueness of static metric extensions for the Bartnik data induced by Schwarzschild coordinate spheres in all dimensions less than 8. This is based on joint work Ye-Kai Wang of NYCU.
Meeting number (access code): 2512 436 3042
Meeting password: AZenac2gd37
