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

TL;DR

This paper proves a Penrose-type inequality involving angular momenta for certain four-dimensional black hole initial data with 3-sphere horizons, characterizing equality cases as Myers-Perry black holes.

Contribution

It establishes a new inequality relating mass, angular momentum, and horizon topology for 4D black holes with 3-sphere horizons, extending previous results.

Findings

Proves a Penrose-type inequality with angular momenta.

Shows equality iff the data is a Myers-Perry black hole.

Extends geometric inequalities to 4D black holes with 3-sphere topology.

Abstract

We establish a Penrose-type inequality with angular momenta 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.