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Analytical study of superradiant instability of the five-dimensional Kerr–Gödel black hole

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Abstract

We present an analytical study of the superradiant instability of the rotating asymptotically Gödel black hole (Kerr–Gödel black hole) in five-dimensional minimal supergravity theory. By employing the matched asymptotic expansion method to solve the Klein–Gordon equation of a scalar field perturbation, we show that the complex parts of quasinormal frequencies are positive in the regime of superradiance. This implies a growing instability of superradiant modes. The reason for this kind of instability is the Dirichlet boundary condition at asymptotic infinity, which is similar to that of rotating black holes in anti-de Sitter (AdS) spacetime.

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Acknowledgements

The author would like to thank Ming-Fan Li for reading the manuscript and useful comments. This work was supported by NSFC, China (Grant No. 11147145 and No. 11205048).

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  1. Department of Physics, Henan Normal University, Xinxiang, 453007, China

    Ran Li

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  1. Ran Li
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Correspondence to Ran Li.

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Li, R. Analytical study of superradiant instability of the five-dimensional Kerr–Gödel black hole. Eur. Phys. J. C 73, 2274 (2013). https://doi.org/10.1140/epjc/s10052-012-2274-9

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  • DOI: https://doi.org/10.1140/epjc/s10052-012-2274-9

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