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arXiv · 1306.0206

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

Marcus A Khuri·Sumio Yamada·Gilbert Weinstein
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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 $|q|\leq r$, 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: $r\geq m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\leq m + \sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural generalization of the Riemannian Penrose inequality: $m\geq 1/2(r+q^2/r)$.

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Marcus A Khuri, Sumio Yamada, Gilbert Weinstein. 2013-06-02. On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture. https://arxiv.org/abs/1306.0206

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