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

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arxiv 1404.6309 v2 pith:VZ5PAZPZ submitted 2014-04-25 gr-qc

classification gr-qc
keywords blackd-dimensionalfieldholemirrorreissner-nordstrscalarboxed
verification ladder T0 review T1 audit T2 compute T3 formal
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We analytically study the superradiant instability of a charged massless scalar field in the background of D-dimensional Reissner-Nordstr\"{o}m (RN) black hole caused by the mirror's boundary condition. By using the asymptotic matching method to solve the Klein-Gordon equation that govern the dynamics of the scalar field, we have derived the expressions of the complex parts of the boxed quasinormal frequencies, and shown they are positive in the regime of superradiance. This indicates the charged scalar field is unstable in D-dimensional Reissner-Nordstr\"{o}m (RN) black hole surrounded by mirror. The numerical work to calculate the boxed quasinormal frequencies in this system is still required in the future.

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