The inequality between mass and angular momentum for axially symmetric black holes

TL;DR

This paper discusses the physical significance of the inequality relating mass and angular momentum in axially symmetric black holes, proves it for a single spinning black hole, and explores implications for black hole stability.

Contribution

It provides a proof of the mass-angular momentum inequality for one spinning black hole and characterizes the extreme Kerr black hole as a mass minimum.

Findings

Proof of the inequality for a single spinning black hole

Characterization of the extreme Kerr black hole as a mass minimum

Implications for black hole stability conjectures

Abstract

In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture on the physical implications of this characterization for the non linear stability problem for black holes.