Quasinormal resonances of a charged scalar field in a charged Reissner-Nordström black hole spacetime: A WKB analysis

Abstract

The fundamental quasinormal resonances of charged Reissner-Nordström black holes due to charged scalar perturbations are derived {\it analytically}. In the WKB regime, $qQ\gg \hslash$, we obtain a simple expression for the fundamental quasinormal resonances: $\omega =qQ/r_{+}-i2\pi T_{\text{BH}}(n+\frac{1}{2})$, where $T_{\text{BH}}$ and $Q$ are the temperature and electric charge of the black hole and $q$ is the electric charge of the field. Remarkably, our results show that the relaxation dynamics of a perturbed Reissner-Nordström black hole may saturate the recently proposed universal relaxation bound.

5 pages. arXiv admin note: text overlap with arXiv:1109.4080

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