The Riemannian Penrose Inequality with Charge for Multiple Black Holes

TL;DR

This paper proves a version of the Riemannian Penrose inequality with charge for multiple black holes, establishing a fundamental relation between mass, charge, and horizon area in Einstein-Maxwell initial data.

Contribution

It extends the Riemannian Penrose inequality with charge to cases with multiple black holes and possibly disconnected horizons, under specific energy and matter conditions.

Findings

Proves the inequality $r \,\leq\, m + \sqrt{m^2 - q^2}$ for multiple black holes.

Establishes the inequality for initial data with possibly disconnected horizons.

Validates the inequality under the charged dominant energy condition with no external charged matter.

Abstract

We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4\pi r^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einstein-Maxwell equations, satisfying the charged dominant energy condition, with no charged matter outside the horizon.