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In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined anapproach to prove the Penrose inequality for general initial data sets of theEinstein equations. In this paper we extend this approach so that it may beapplied to a charged version of the Penrose inequality. Moreover, assuming thatthe initial data is time symmetric, we prove the rigidity statement in the caseof equality for the charged Penrose inequality, a result which seems to beabsent from the literature. A new quasi-local mass, tailored to charged initialdata sets is also introduced, and used in the proof.

On the Penrose Inequality for Charged Black Holes