Emergence of Apparent Horizon in Gravitational Collapse
Abstract
We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smooth (except at that point) and spacelike. In the proof we employ a scale critical trapped surface formation criterion established by An and Luk and a new type of quasilinear elliptic equation is studied. The main conclusion of this paper proves a conjecture of Ashtekar on black hole thermodynamics. And the spacetimes constructed here could also be viewed as (non-spherically symmetric) generalizations of the well-known Vaidya spacetime.
Keywords
Cite
@article{arxiv.1703.00118,
title = {Emergence of Apparent Horizon in Gravitational Collapse},
author = {Xinliang An},
journal= {arXiv preprint arXiv:1703.00118},
year = {2020}
}
Comments
63 pages; to appear in Ann. PDE 6 (2020)