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

TL;DR

This paper proposes using all three types of resonance modes—quasinormal, total transmission, and total reflection modes—in the highly damped regime to derive the quantized, equally spaced entropy spectrum of Kerr and Reissner-Nordstrom black holes, aligning with Bekenstein's proposal.

Contribution

It introduces a unified approach using all resonance modes to derive the black hole entropy spectrum, resolving inconsistencies in previous methods.

Findings

TRM yields a simple, equally spaced outer horizon area spectrum.

Kerr black hole has a universal, equally spaced entropy spectrum.

Reissner-Nordstrom black hole also exhibits an equally spaced entropy spectrum.

Abstract

Since the Bekenstein's proposal that a black hole has equally spaced area spectrum, the quasinormal modes as the characteristic modes of a black hole have been used in 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 the Bekenstein's proposal. In this paper, noting that black holes can have three types of resonance modes which are quasinormal modes (QNM), total transmission modes (TTM), and total reflection modes (TRM), we propose that all of these modes in 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 action variable, we find a very simple result from the TRM. It gives equally spaced outer horizon area. Therefore by 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-Nordstrom black hole also has equally spaced entropy spectrum.