Existence of Black Holes Due to Concentration of Angular Momentum

TL;DR

This paper establishes a universal inequality linking size and angular momentum, providing a new sufficient condition for black hole formation in axisymmetric Einstein initial data.

Contribution

It introduces a novel inequality relating angular momentum and size, expanding criteria for black hole existence beyond mass concentration.

Findings

Proves a universal inequality for angular momentum and size in axisymmetric data

Provides a new sufficient condition for black hole formation

Compared with traditional mass concentration criteria

Abstract

We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which satisfy an appropriate energy condition. A brief comparison is also made with more traditional black hole existence criteria based on concentration of mass.