Analytic study of superradiant stability of Kerr-Newman black holes under charged massive scalar perturbation

TL;DR

This paper analyzes the conditions under which Kerr-Newman black holes remain stable against charged massive scalar perturbations, revealing specific horizon and charge-to-mass ratio criteria for superradiant stability.

Contribution

It provides a detailed effective potential analysis to identify stability conditions for Kerr-Newman black holes under charged scalar perturbations, a novel stability criterion.

Findings

Stability when horizon ratio $r_-/r_+ \, \leqslant \, 1/3$

Stability when charge-to-mass ratio $q/\mu \times Q/M > 1$

Derived effective potential conditions for superradiant stability.

Abstract

The superradiant stability of a Kerr-Newman black hole and charged massive scalar perturbation is investigated. We treat the black hole as a background geometry and study the equation of motion of the scalar perturbation. From the radial equation of motion, we derive the effective potential experienced by the scalar perturbation. By a careful analysis of this effective potential, it is found that when the inner and outer horizons of Kerr-Newman black hole satisfy $\frac{r_-}{r_+}\leqslant\frac{1}{3}$ and the charge-to-mass ratios of scalar perturbation and black hole satisfy $ \frac{q}{\mu }\frac{Q}{ M}>1 $, the Kerr-Newman black hole and scalar perturbation system is superradiantly stable.