On the Penrose inequality

TL;DR

This paper proposes a new approach to proving the Penrose inequality by leveraging the four-dimensional spacetime structure, potentially leading to a rigorous proof in the general case.

Contribution

It introduces a novel argument that extends previous methods by removing initial data restrictions and utilizing spacetime geometry.

Findings

Suggests a promising direction for a rigorous proof of the Penrose inequality.

Builds on Geroch's and Jang-Wald's methods with a new spacetime-based approach.

Provides conceptual insights that could unify existing partial results.

Abstract

The purpose of this letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive energy theorem which was later adapted by Jang and Wald to apply to initial data sets containing apparent horizons. The new input is to dispense with the a priori restriction to an initial data set and to use the four-dimensional structure of spacetime in an essential way.