A universal inequality for axisymmetric and stationary black holes with surrounding matter in the Einstein-Maxwell theory

TL;DR

This paper proves a universal inequality relating angular momentum, electric charge, and horizon area for sub-extremal axisymmetric, stationary black holes with surrounding matter in Einstein-Maxwell theory, extending understanding of black hole properties.

Contribution

It establishes a new universal inequality for black holes with matter, generalizing previous results to include surrounding matter in Einstein-Maxwell theory.

Findings

The inequality $(8 ext{pi} J)^2+(4 ext{pi} Q^2)^2 < A^2$ holds for sub-extremal black holes.

The result applies to black holes with arbitrary surrounding matter.

It advances theoretical understanding of black hole parameter constraints.

Abstract

We prove that in Einstein-Maxwell theory the inequality $(8\pi J)^2+(4\pi Q^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum, electric charge, and horizon area of the black hole, respectively.