On the Penrose Inequality for Charged Black Holes

TL;DR

This paper extends Bray and Khuri's approach to prove a charged version of the Penrose inequality for initial data sets in general relativity, introducing a new quasi-local mass concept and establishing rigidity in the time symmetric case.

Contribution

It develops a method to prove the charged Penrose inequality and introduces a new quasi-local mass, also proving rigidity for the equality case under time symmetry.

Findings

Proved the charged Penrose inequality for initial data sets.

Introduced a new quasi-local mass for charged data.

Established rigidity in the time symmetric case.

Abstract

In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein equations. In this paper we extend this approach so that it may be applied to a charged version of the Penrose inequality. Moreover, assuming that the initial data is time symmetric, we prove the rigidity statement in the case of equality for the charged Penrose inequality, a result which seems to be absent from the literature. A new quasi-local mass, tailored to charged initial data sets is also introduced, and used in the proof.