Proof of the angular momentum-mass inequality for axisymmetric black holes

TL;DR

This paper proves that for a class of axisymmetric black hole initial data, the extreme Kerr solution uniquely minimizes mass for fixed angular momentum, confirming the angular momentum-mass inequality in general relativity.

Contribution

It establishes the uniqueness of the extreme Kerr initial data as the minimal mass configuration for fixed angular momentum in a broad class of black hole spacetimes.

Findings

Extreme Kerr data is the unique minimum of mass for fixed angular momentum.

All data in the class satisfy the inequality √J ≤ m.

The proof confirms the angular momentum-mass inequality for axisymmetric black holes.

Abstract

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence, we obtain that any data in this class satisfy the inequality $\sqrt{J} \leq m$, where $m$ and $J$ are the total mass and angular momentum of the spacetime.