Abstract

The positive mass theorem is one of the fundamental results in general relativity. It states that the total mass of asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the cosmic censorship conjecture in general relativity. Recently, Lu and Miao proved a quasi-local Penrose inequality for the quasi-local energy with reference in the Schwarzschild manifold. In this article, we prove a quasi-local Penrose inequality for the quasi-local energy with reference in any spherically symmetric static spacetime.