Entropy spectra of black holes from resonance modes in scattering by the black holes

Abstract

Since Bekenstein's proposal that a black hole has an equally spaced area spectrum, the quasinormal modes (QNM) as the characteristic modes of a black hole have been used for obtaining the horizon area spectrum of the black hole. However, the area spectrum of the Kerr black hole in some previous works was inconsistent with Bekenstein's proposal. In this paper, noting that black holes can have three types of resonance modes which are QNM, total transmission modes (TTM), and total reflection modes (TRM), we propose that all of these modes in a highly damped regime should be used in quantizing the black hole. Although the QNM and the TTM of the Kerr black hole give us complicated quantization conditions from the Bohr–Sommerfeld quantization of an action variable, we find a very simple result from the TRM. It gives an equally spaced outer horizon area. Therefore, by the Bekenstein–Hawking area law, we find that the Kerr black hole has universal behavior of the equally spaced entropy spectrum. With the same argument, we find that the Reissner–Nordström black hole also has the equally spaced entropy spectrum.