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.
Categories: gr-qc math-ph math.DG math.MP