The Penrose Inequality in Higher Dimensional Spherically Symmetric Spacetimes

In this paper, we give a preliminary proof of the Penrose inequality for charged and asymptotically flat spacetimes in higher dimensions under the spherically symmetry and without Riemannian assumption. For the most part, our steps and arguments are based on method carried out by Malec and Murchadha to prove the inequality in four dimensional case. To do so, we propose a quasilocal mass in higher dimensional spacetimes and show that it plays such an important role to establish the inequaliry in our case.