A quasi-local Penrose inequality for the quasi-local energy with static references

Chen, Po-Ning

doi:10.1090/tran/8158

A quasi-local Penrose inequality for the quasi-local energy with static references
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Abstract:

The positive mass theorem is one of the fundamental results in geometric analysis and mathematical general relativity. It states that, assuming the dominant energy condition (i.e., nonnegative scalar curvature) then the total mass of an asymptotically flat spacetime is nonnegative. The Penrose inequality provides a lower bound on mass by the area of the black hole. Lu and Miao proved a quasi-local Penrose inequality for the quasi-local energy using the Schwarzschild manifold as a comparison manifold. In this article, we prove a quasi-local Penrose inequality for the quasi-local energy using any spherically symmetric static spacetime as the comparison manifold. Moreover, in the equality case, the manifold must be isometric to the comparison manifold, which has to be the Schwarzschild manifold.

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