Tightening the Penrose Inequality

TL;DR

This paper introduces a new Penrose-like inequality for static black holes that incorporates mass, horizon area, and temperature, providing a tighter bound than the traditional Penrose inequality.

Contribution

It proposes a novel inequality involving black hole parameters, proven under specific energy conditions, and includes known inequalities as special cases.

Findings

The new inequality is saturated by Schwarzschild and Reissner-Nordstr"om black holes.

It is tighter than the traditional Penrose inequality for extremal black holes.

The proof assumes null and trace energy conditions in the spherically symmetric case.

Abstract

The Penrose inequality estimates the lower bound of the mass of a black hole in terms of the area of its horizon. This bound is relatively loose for extremal or near extremal black holes. We propose a new Penrose-like inequality for static black holes involving the mass, area of the black hole event horizon and temperature. Our inequality includes the Penrose inequality as its corollary, and it is saturated by both the Schwarzschild and Reissner-Nordstr\"om black holes. In the spherically-symmetric case, we prove this new inequality by assuming both the null and trace energy conditions.