Quantization of Black Hole Entropy from Quasinormal Modes

TL;DR

This paper calculates the quantum spectra of black hole entropy using quasinormal modes and proposes that entropy levels are equally spaced and independent of spacetime dimension, while area spacing varies with gravity theory.

Contribution

It introduces a new interpretation of quasinormal modes to derive black hole entropy spectra and conjectures universal entropy spacing across different black hole types.

Findings

Entropy spectrum is equally spaced and dimension-independent.

Area spectrum spacing depends on the gravity theory.

Results align with previous findings by Kothawala et al.

Abstract

In Phys. Rev. D 78 (2008) 104018 [arXiv:0807.1481], the conclusion that "entropy eigenvalues of GB black hole are discrete and equally spaced, but the area spacing is not equidistant" was firstly presented by Kothawala, Padmanabhan and Sarkar. In this paper, using the new physical interpretation of quasinormal modes proposed by Maggiore, we calculate the quantum spectra of entropy for various types of non-rotating black holes with no charge. The spectrum is obtained by imposing Bohr-Sommerfeld quantization condition to the adiabatic invariant quantity. We conjecture that the spacing of entropy spectrum is equidistant and is independent of the dimension of spacetime. However, the spacing of area spectrum depends on gravity theory. In Einstein's gravity, it is equally spaced, otherwise it is non-equidistant. This conjecture agrees with the result of Kothawala, Padmanabhan and Sarkar.