Periodicity and area spectrum of black holes

TL;DR

This paper confirms that the periodicity of black holes can explain their area quantization, deriving equally spaced area spectra for Schwarzschild and Kerr black holes using wave period analysis without small angular momentum assumptions.

Contribution

It introduces a method to derive black hole area spectra based on wave periodicity, applicable to both Schwarzschild and Kerr black holes without simplifying assumptions.

Findings

Equal area spacing for Schwarzschild and Kerr black holes.

Method reproduces known spectra without small angular momentum approximation.

Supports Maggiore's speculation on black hole periodicity and area quantization.

Abstract

The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momentum assumption, which is necessary from the perspective of quasinormal mode, is not employed as the general area spacing is reproduced.