Higher dimensional Penrose inequality in spherically symmetric spacetime

Abstract

We prove the higher dimensional charged Penrose inequality conjecture on a spacetime where the initial geometry is spherically symmetric using the definition of a quasi-local mass in higher dimensional spacetime. Some physical assumptions on the initial spacetime and on its hypersurface have been taken in order to avoid the real singularity. We also impose two physical conditions on matter such as the dominant energy condition and the localization of the matter distribution.