A Penrose-type inequality with angular momenta for black holes with 3-sphere horizon topology

Abstract

We establish a Penrose-type inequality with angular momentum for four dimensional, biaxially symmetric, maximal, asymptotically flat initial data sets (M, g, k) for the Einstein equations with fixed angular momenta and horizon inner boundary associated to a 3-sphere outermost minimal surface. Moreover, equality holds if and only if the initial data set is isometric to a canonical time slice of a stationary Myers-Perry black hole.