Spectroscopy of a Reissner-Nordstr\"{o}m black hole via an action variable

TL;DR

This paper derives an evenly spaced area spectrum for Reissner-Nordström black holes using an adiabatic invariant approach, showing the spectrum's independence from black hole parameters and avoiding the small charge approximation.

Contribution

It introduces a method to determine the black hole area spectrum via an action variable and quantization rule, applicable to charged black holes without small charge restrictions.

Findings

Reissner-Nordström black hole has an evenly spaced area spectrum.

The area spacing equals that of a Schwarzschild black hole, 8π.

The spectrum is independent of the black hole's charge and parameters.

Abstract

With the help of the Bohr--Sommerfeld quantization rule, the area spectrum of a charged, spherically symmetric spacetime is obtained by studying an adiabatic invariant action variable. The period of the Einstein-Maxwell system, which is related to the surface gravity of a given spacetime, is determined by the Kruskal--like coordinates. It is shown that the area spectrum of the Reissner-Nordstr\"{o}m black hole is evenly spaced and the spacing is the same as that of a Schwarzschild black hole, which indicates that the area spectrum of a black hole is independent of its parameters. In contrast to the quasi-normal mode analysis, we do not impose the small charge limit as the general area gap $8\pi $ is obtained.