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

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.