Quasinormal Spectrum and Quantization of Charged Black Holes

TL;DR

This paper analytically derives the asymptotic quasinormal mode spectrum of charged scalar fields in Reissner-Nordström black holes, linking it to black hole quantization and fundamental area units.

Contribution

It provides an explicit analytic expression for the quasinormal modes of charged black holes, connecting these resonances to black hole thermodynamics and quantum area quantization.

Findings

Analytic formula for charged black hole quasinormal modes.

Link between quasinormal frequencies and black hole area quantization.

Asymptotic resonance corresponds to a fundamental area unit of 4ħln2.

Abstract

Black-hole quasinormal modes have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We study {\it analytically} the asymptotic quasinormal spectrum of a {\it charged} scalar field in the (charged) Reissner-Nordstr\"om spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature $T_{BH}$, and its electric potential $\Phi$. We discuss the applicability of the results in the context of black-hole quantization. In particular, we show that according to Bohr's correspondence principle, the asymptotic resonance corresponds to a fundamental area unit $\Delta A=4\hbar\ln2$.