Higher dimensional Penrose inequality in spherically symmetric spacetime

• In this paper, we prove the higher dimensional charged Penrose inequality conjecture on spacetimes where the initial geometries are spherically symmetric.
• Some physical assumptions on the initial spacetime and on its hypersurface have been taken in order to avoid the real singularity.
• Then, we define a quasilocal mass in higher dimensional spacetime and further impose two physical condition on matters such as the dominant energy condition and the localization of matter distribution.

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.