Superradiant instability of $D$-dimensional Reissner-Nordström-anti-de Sitter black hole mirror system

Abstract

In this paper, a detailed analysis for superradiant stability of the system composed by a $D$-dimensional Reissner-Nordström-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.

16 pages, 8 figures; v2: minor changes made, some references added; v3: published in Int. J. Mod. Phys. D

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• Analytic study of superradiant stability of Kerr-Newman black holes under charged massive scalar perturbation
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• Penrose process in Reissner-Nordström-AdS black hole spacetimes: Black hole energy factories and black hole bombs
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• No black hole bomb for D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation