A Gibbons-Penrose inequality for surfaces in Schwarzschild spacetime

TL;DR

This paper introduces a geometric inequality for surfaces in Schwarzschild spacetime that supports the Penrose inequality, with proofs in key cases, advancing understanding in mathematical relativity.

Contribution

It proposes a new geometric inequality for surfaces in Schwarzschild spacetime that implies the Penrose inequality, with proofs in several important cases.

Findings

The inequality holds in several key cases.

It implies the Penrose inequality for collapsing dust shells.

Supports conjectures in mathematical relativity.

Abstract

We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.