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arXiv · 1703.00118

Emergence of Apparent Horizon in Gravitational Collapse

Xinliang An
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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.

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Xinliang An. 2017-03-01. Emergence of Apparent Horizon in Gravitational Collapse. https://doi.org/10.1007/s40818-020-00085-9

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