Spectroscopy of a Reissner–Nordström 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 Kruskal-like coordinates. It is shown that the area spectrum of the Reissner–Nordström 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 quasi-normal mode analysis, we do not impose the small charge limit, as the general area gap 8π is obtained.