Attractive gravity probe surfaces in higher dimensions

TL;DR

This paper generalizes the Riemannian Penrose inequality to higher dimensions by introducing a parameterized refined attractive gravity probe surface, establishing an area inequality applicable in both strong and weak gravity regimes.

Contribution

It introduces a new class of refined AGPS with a parameter lpha, extending the area inequality to higher dimensions and different gravitational regimes.

Findings

Derived an area inequality for refined AGPS in higher dimensions.

Applicable to surfaces in both strong and weak gravity regions.

Generalized the Penrose inequality beyond four dimensions.

Abstract

A generalization of the Riemannian Penrose inequality in $n$-dimensional space ($3\le n<8$) is done. We introduce a parameter $\alpha$ ($-\frac{1}{n-1}<\alpha < \infty$) indicating the strength of the gravitational field, and define a refined attractive gravity probe surface (refined AGPS) with $\alpha$. Then, we show the area inequality for a refined AGPS, $A \le \omega_{n-1} \left[ (n+2(n-1)\alpha)Gm /(1+(n-1)\alpha) \right]^{\frac{n-1}{n-2}}$, where $A$ is the area of the refined AGPS, $\omega_{n-1}$ is the area of the standard unit $(n-1)$-sphere, $G$ is Newton's gravitational constant and $m$ is the Arnowitt-Deser-Misner mass. The obtained inequality is applicable not only to surfaces in strong gravity regions such as a minimal surface (corresponding to the limit $\alpha \to \infty$), but also to those in weak gravity existing near infinity (corresponding to the limit $\alpha \to -\frac{1}{n-1}$).