A localized spacetime Penrose inequality and horizon detection with quasi-local mass

TL;DR

This paper establishes a new quasi-local Penrose inequality relating boundary quasi-local mass and horizon area, providing criteria for the existence of marginally outer trapped surfaces in initial data sets.

Contribution

It introduces a comparison theorem between Wang/Liu-Yau and Hawking masses in Jang graphs, leading to a localized Penrose inequality and horizon detection conditions.

Findings

Proved a comparison theorem between quasi-local and Hawking masses.

Established a quasi-local Penrose inequality involving boundary mass and horizon area.

Provided conditions for the existence or non-existence of marginally outer trapped surfaces.

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.