A universal inequality between angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

TL;DR

This paper proves a universal inequality relating the angular momentum and horizon area of sub-extremal axisymmetric, stationary black holes with surrounding matter, establishing a fundamental geometric constraint.

Contribution

It establishes a new universal inequality $8\pi|J|<A$ for black holes with matter, extending previous results to more general astrophysical scenarios.

Findings

The inequality holds for black holes with arbitrary surrounding matter.

It applies to sub-extremal, axisymmetric, stationary black holes.

The result generalizes known inequalities to more realistic conditions.

Abstract

We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8\pi|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.