On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture

Abstract

We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\le r$, where $q$ is the total charge and $r=\sqrt{A/4\pi }$ is the area radius of $S$. A consequence of this inequality is that for connected black holes the following lower bound on the area holds: $r\ge m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\le m+\sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural generalization of the Riemannian Penrose inequality: $m\ge 1/2(r+q^2/r)$.

4 pages; 1st revision, added a generalization, added a reference; 2nd revision, minor corrections

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