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BIMSA General Relativity Seminar
On the blowup of regularized solutions to the Jang equation and constant expansion surfaces
On the blowup of regularized solutions to the Jang equation and constant expansion surfaces
Organizers
Speaker
Kai-wei Zhao
Time
Monday, August 19, 2024 4:00 PM - 5:30 PM
Venue
Online
Online
Zoom 559 700 6085
(BIMSA)
Abstract
In the celebrated series of papers, Schoen-Yau first completed the proof of spacetime Positive Energy Theorem by reducing it to the time-symmetric (Riemannian) case using the Jang equation. To acquire solutions to the Jang equation, they introduced a family of regularized equations and took the limit of regularized solutions, whereas a sequence of regularized solutions could blow up in some bounded regions enclosed by apparent horizons, which can be interpreted as black hole regions. They analyzed the blowup behavior near and outside the apparent horizons, but what happens inside was unknown. In this presentation, we will talk about the blowup behavior inside apparent horizons through dilation and translation. The geometry of limits of properly blowdown and properly translated regularized solutions is closely related to constance null expansion surfaces. In addition, we will explore the structure of black hole regions. As applications, we give a lower estimate for ADM mass in terms of a quasi-local quantity of the curvature of initial data set and, in the very slow blowup case, we give a topological restriction on black hole regions.