A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

TL;DR

This paper establishes a universal relation between charge and rotation rate for degenerate black holes with surrounding matter, extending known solutions to more complex astrophysical scenarios.

Contribution

It demonstrates that the relation a^2 + Q^2 = M^2 holds for a broad class of black hole solutions with matter, generalizing the Kerr-Newman case.

Findings

Universal charge-rotation constraint for degenerate black holes.

Extension of Kerr-Newman solution to matter-surrounded black holes.

Validity of the relation under continuous spacetime sequences.

Abstract

We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.