Abstract
We study the superradiance instability of charged massive scalar field in the background of Kerr–Newman–anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein–Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr–Newman–anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
Highlights
In an rotating charged black hole with ergosphere outside the event horizon, the impinging bosonic fields with frequency ω, angular momentum m, and electric charge e inside a specific band 0 < ω < mΩH + eΦH, (1)where ΩH is angular velocity of event horizon, and ΦH is electrostatic potential at horizon, can be scattered off with a higher amplitude
The asymptotically flat Kerr and Kerr-Newman black holes have this kind of instability against massive scalar field perturbations, where the effective reflective mirror is sourced from mass terms [10, 11, 12, 13]
We have studied the instability of small KN-anti-de Sitter (AdS) black hole caused by the superradiance of scalar field
Summary
In an rotating charged black hole with ergosphere outside the event horizon, the impinging bosonic fields with frequency ω, angular momentum m, and electric charge e inside a specific band 0 < ω < mΩH + eΦH ,. The asymptotically flat Kerr and Kerr-Newman black holes have this kind of instability against massive scalar field perturbations, where the effective reflective mirror is sourced from mass terms [10, 11, 12, 13]. For the rotating black hole in anti-de Sitter (AdS) space, the boundary of AdS spacetime behaves as reflecting mirror and superradiant modes can be bounded in the effective potential barrier, which leads to instability of black hole. It is found by Cardoso and Dias [16] that the small Kerr-AdS black hole is unstable against massless scalar field perturbation.
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