Horizon area--angular momentum inequality for a class of axially symmetric black holes

TL;DR

This paper proves an inequality relating the horizon area and angular momentum for a broad class of axially symmetric black holes, including highly distorted and extreme cases, with implications for numerical simulations.

Contribution

It establishes a new inequality for horizon area and angular momentum applicable to a wide class of black holes, extending previous results to more general initial data.

Findings

Proved area-angular momentum inequality for axially symmetric black holes.

Extended inequality to extreme throat initial data.

Applicable to highly distorted black holes in numerical evolutions.

Abstract

We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a two-surface. These initial conditions have been extensively used in the numerical evolution of rotating black holes. They can describe highly distorted black holes, not necessarily near equilibrium. We also prove the inequality on extreme throat initial data, extending previous results.