Superradiance Instability of Small Rotating AdS Black Holes in Arbitrary Dimensions

Abstract

We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance instability irrespective of the value of the (positive) angular momentum quantum number. To do this we solve the Klein-Gordon equation in the slow rotation, low frequency limit. By using the asymptotic matching technique, we are able to calculate the real and imaginary parts of the correction terms to the frequency of the scalar field due to the presence of the black hole, confirming the presence of superradiance instability. We see that, unlike in the case of static AdS black holes, the analytical method is valid for rotating AdS black holes for any value of angular momentum number and space-time dimensions. For comparison we derive the corresponding correction terms for Myers-Perry black holes in the black hole bomb formalism in Appendix and see that the results are in agreement.

18 pages, V2: Several typos corrected, references added, Published version

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• Weak Cosmic Censorship Conjecture in Kerr-(Anti-)de Sitter Black Hole with Scalar Field
• Massive Scalar Perturbations on Myers-Perry-de Sitter Black Holes with a Single Rotation
• Weak Cosmic Censorship with Pressure and Volume in Charged Anti-de Sitter Black Hole under Charged Scalar Field
• Superradiance in the BTZ black hole with Robin boundary conditions
• Weak Cosmic Censorship Conjecture in Kerr-Newman-(Anti-)de Sitter Black Hole with Charged Scalar Field
• Superradiant stability of the Kerr black holes
• Superradiant instability of $D$-dimensional Reissner-Nordström-anti-de Sitter black hole mirror system
• Superradiance of a Global Monopole in Reissner-Nordström(-AdS) Space-time
• No black hole bomb for D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation
• Superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes
• Thermodynamics of spinning AdS4 black holes in gauged supergravity