On the Penrose inequality in anti-deSitter space

TL;DR

This paper formulates a Penrose inequality for asymptotically anti-deSitter spacetimes and demonstrates its validity for time asymmetric, spherically symmetric data, extending the inequality's applicability beyond flat spacetimes.

Contribution

It introduces a new formulation of the Penrose inequality for AAdS spacetimes and proves its validity in a specific symmetric case.

Findings

The inequality holds for time asymmetric data in spherical symmetry.

The formulation is motivated by the constant-negative-curvature AdS black hole metric.

Provides a potential test for cosmic censorship in AAdS spacetimes.

Abstract

For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.