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.
M. Khuri acknowledges the support of NSF Grants DMS-1007156 and DMS-1308753. S. Yamada acknowledges the support of JSPS Grants 23654061 and 24340009.
"Proof of the Riemannian Penrose inequality with charge for multiple black holes." J. Differential Geom. 106 (3) 451 - 498, July 2017. https://doi.org/10.4310/jdg/1500084023