Proof of the Riemannian Penrose Inequality with Charge for Multiple Black Holes

TL;DR

This paper proves the Riemannian Penrose inequality with charge for multiple black holes in Einstein-Maxwell theory, extending previous methods to more complex configurations without charged matter outside horizons.

Contribution

It generalizes Bray's conformal flow method to handle multiple black holes with charge, providing a new proof of the inequality in this setting.

Findings

Validates the inequality for multiple black holes with charge

Extends conformal flow techniques to charged scenarios

Supports the cosmic censorship conjecture in this context

Abstract

We present a proof of the Riemannian Penrose inequality with charge in the context of asymptotically flat initial data sets for the Einstein-Maxwell equations, having possibly multiple black holes with no charged matter outside the horizon, and satisfying the relevant dominant energy condition. The proof is based on a generalization of Hubert Bray's conformal flow of metrics adapted to this setting.