Relaxation dynamics of charged gravitational collapse

TL;DR

This paper derives an analytical formula for the fundamental quasinormal modes of near-extremal charged black holes, linking the relaxation dynamics of charged fields to black hole parameters such as temperature and electric potential.

Contribution

It provides a simple analytic expression for quasinormal resonances of near-extremal Reissner-Nordström black holes, enhancing understanding of their relaxation dynamics.

Findings

Derived an explicit formula for quasinormal frequencies.

Linked relaxation times to black hole temperature and potential.

Applicable to near-extremal charged black holes.

Abstract

We study analytically the relaxation dynamics of charged test fields left outside a newly born charged black hole. In particular, we obtain a simple analytic expression for the fundamental quasinormal resonances of near-extremal Reissner-Nordstr\"om black holes. The formula is expressed in terms of the black-hole physical parameters: $\omega=q\Phi-i2\pi T_{BH}(n+{1 \over 2})$, where $T_{BH}$ and $\Phi$ are the temperature and electric potential of the black hole, and $q$ is the charge of the field.