  The positive mass theorem is one of the fundamental results in general
relativity. It states that, assuming the dominant energy condition, the total
mass of an 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. In
[14], 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.

Differential Geometry;General Relativity and Quantum Cosmology