On the Riemannian Penrose inequality in dimensions less than 8

TL;DR

This paper extends Bray's technique to prove the Riemannian Penrose inequality for dimensions less than 8, providing a key step in understanding mass bounds in higher-dimensional geometries with black holes.

Contribution

The paper generalizes Bray's method to dimensions under 8, advancing the proof of the Riemannian Penrose inequality in higher-dimensional manifolds.

Findings

Extended Bray's technique to dimensions less than 8

Proved the Riemannian Penrose inequality in these dimensions

Enhanced understanding of mass bounds in higher-dimensional gravity

Abstract

The Positive Mass Theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass. The Riemannian Penrose inequality provides a sharp lower bound for the mass when black holes are present. More precisely, this lower bound is given in terms of the area of an outermost minimal surface, and equality is achieved only for Schwarzschild metrics. The Riemannian Penrose inequality was first proved in three dimensions in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole. In 1999, H. Bray extended this result to the general case of multiple black holes using a different technique. In this paper we extend Bray's technique to dimensions less than 8.