Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

TL;DR

This paper provides numerical evidence supporting the inequality relating total mass and angular momentum in multiple axially symmetric black holes, and shows no regular equilibrium solutions for two extreme black holes.

Contribution

It introduces a numerical method using parabolic heat flow to verify the mass-angular momentum inequality and investigates the non-existence of certain equilibrium black hole solutions.

Findings

Mass-angular momentum inequality holds numerically.

No regular solutions for two extreme black holes in equilibrium.

Method demonstrates effectiveness for axially symmetric Einstein equations.

Abstract

We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (non-stationary) black holes. We use a parabolic heat flow to solve numerically the stationary axially symmetric Einstein equations. As a by product our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.