The Riemannian Penrose inequality and a virtual gravitational collapse

TL;DR

This paper reinterprets Bray's proof of the Riemannian Penrose inequality, revealing a connection to Lorentzian metrics and exploring potential extensions to charged black holes.

Contribution

It provides a novel reinterpretation of Bray's proof linking Riemannian and Lorentzian geometries and suggests extensions to charged black hole scenarios.

Findings

Flow of Riemannian metrics yields Lorentzian spacetime metrics.

Potential extension to charged black hole cases.

New geometric insights into gravitational collapse.

Abstract

We reinterpret the proof of the Riemannian Penrose inequality by H. Bray. The modified argument turns out to have a nice feature so that the flow of Riemannian metrics appearing Bray's proof gives a Lorentzian metric of a spacetime. We also discuss a possible extension of our approach to charged black holes.