On the Penrose Inequality for general horizons

TL;DR

This paper proves the Penrose inequality for a broad class of initial data in general relativity, extending previous results by relaxing horizon conditions and using inverse mean curvature flow techniques.

Contribution

It generalizes Geroch's proof by applying inverse mean curvature flow to non-minimal horizons under certain data restrictions.

Findings

Penrose inequality holds for general horizons under specified conditions

Extension of monotonicity of Hawking mass beyond minimal surfaces

Local adjustments of initial data can satisfy the necessary conditions

Abstract

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.