Tightening the Penrose Inequality

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 not very ``tight'' for extremal or near extremal black holes. We propose a new Penrose-like inequality for static black holes involving the mass, the area of black hole event horizon and the temperature. Our inequality includes the Penrose inequality as its corollary and it is saturated by both the Schwarzschild black hole and Reissner-Nordstr\"om (RN) black hole. In the spherically-symmetric case, we prove this new inequality by assuming both the null and trace energy conditions.Comment: latex, 19 page