Superradiant instability of $D$-dimensional Reissner-Nordstr\"{o}m-anti-de Sitter black hole mirror system

TL;DR

This paper investigates the superradiant stability of higher-dimensional Reissner-Nordström-anti-de Sitter black holes with a mirror, revealing how parameters like mirror radius, scalar mass, and spacetime dimension influence stability and instability regimes.

Contribution

It provides a detailed analysis of superradiant stability in higher-dimensional RN-AdS black holes with a mirror, highlighting the effects of various parameters on stability and instability.

Findings

Stability is heavily influenced by mirror radius, scalar mass, AdS radius, and spacetime dimension.

Higher dimensions weaken the degree of superradiant instability.

Small RN-AdS black holes can be unstable, while large ones tend to be stable.

Abstract

In this paper, a detailed analysis for superradiant stability of the system composed by a $D$-dimensional Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS) black hole and a reflecting mirror under charged scalar perturbations are presented in the linear regime. It is found that the stability of the system is heavily affected by the mirror radius as well as the mass of the scalar perturbation, AdS radius and the dimension of space-time. In a higher dimensional space-time, the degree of instability of the superradiant modes will be severely weakened. Nevertheless, the degree of instability can be magnified significantly by choosing a suitable value of the mirror radius. Remarkably, when the mirror radius is smaller than a threshold value the system becomes stable. We also find that massive charged scalar fields cannot trigger the instabilities in the background of $D$-dimensional asymptotically flat RN black hole. For a given scalar charge, a small RN-AdS black hole can be superradiantly unstable, while a large one may be always stable under charged scalar field with or without a reflecting mirror. We also show that these results can be easily expounded and understood with the help of factorized potential analysis.