The superradiant stability of Kerr-Newman black holes

TL;DR

This paper investigates the superradiant stability of Kerr-Newman black holes by extending previous stability conditions for Kerr black holes, analyzing scalar perturbations, and deriving new stability criteria based on additional variables.

Contribution

It introduces a new variable to extend superradiant stability results from Kerr to Kerr-Newman black holes, providing refined stability conditions for scalar perturbations.

Findings

Kerr-Newman black holes are superradiantly stable under certain conditions.

The stability condition is expanded to include additional parameters like charge and angular momentum.

New bounds for scalar field frequencies ensuring stability are derived.

Abstract

In this article, the superradiation stability of Kerr-Newman black holes is discussed by introducing the condition used in Kerr black holes y into them. Moreover, the motion equation of the minimal coupled scalar perturbation in a Kerr-Newman black hole is divided into angular and radial parts. Hod proved\cite{12} that the Kerr black hole should be superradiantly stable under massive scalar perturbation when $\mu \ge \sqrt{2}m\Omega_H$, where $\mu$ is the mass. In this article, a new variable y is added here to expand the results of the above article. When $\sqrt{2(a^2+Q^2)}/{r^2_+}< \omega< m\varOmega_H+q\varPhi_H$,particularly $\mu \ge \sqrt{2}(m\varOmega_H+q\varPhi_H)$,so the Kerr-Newman black hole is superradiantly stable at that time.