Mathematics
A localized spacetime Penrose inequality and horizon detection with quasi-local mass
Document Type
Article
Abstract
For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain. Using this, we prove a quasi-local Penrose inequality that involves these quasi-local masses of the boundary and the area of an outermost marginally outer trapped surface (MOTS) in the domain or the area of minimizing minimal surface within the Jang graphs. Moreover, we obtain sufficient conditions for the (non)existence of a MOTS within a domain, in the spirit of the folklore hoop conjecture.
Publication Title
Journal of Differential Geometry
Publication Date
11-2023
Volume
125
Issue
3
First Page
405
Last Page
425
ISSN
0022-040X
DOI
10.4310/jdg/1701804148
Keywords
black holes, initial datum, manifold
Repository Citation
Alaee, Aghil; Lesourd, Martin; and Yau, Shing Tung, "A localized spacetime Penrose inequality and horizon detection with quasi-local mass" (2023). Mathematics. 41.
https://commons.clarku.edu/mathematics/41
