Quasinormal resonances of a charged scalar field in a charged Reissner-Nordstr\"om black hole spacetime: A WKB analysis

TL;DR

This paper derives an analytical expression for the fundamental quasinormal resonances of charged scalar fields in Reissner-Nordström black holes using WKB approximation, revealing insights into black hole relaxation dynamics.

Contribution

It provides a simple analytical formula for charged scalar quasinormal modes in Reissner-Nordström black holes, extending understanding of black hole relaxation behavior.

Findings

Derived an analytical expression for quasinormal frequencies.

Showed the relaxation bound can be saturated.

Connected relaxation dynamics with black hole thermodynamics.

Abstract

The fundamental quasinormal resonances of charged Reissner-Nordstr\"om black holes due to charged scalar perturbations are derived {\it analytically}. In the WKB regime, $qQ\gg\hbar$, we obtain a simple expression for the fundamental quasinormal resonances: $\omega=qQ/r_+-i2\pi T_{\text{BH}}(n+{1 \over 2})$, 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-Nordstr\"om black hole may saturate the recently proposed universal relaxation bound.