Area Spectrum of BTZ Black Holes from the Periodicity in Euclidean Time

TL;DR

This paper investigates the quantization of the horizon area of BTZ black holes using Euclidean time periodicity, confirming equally spaced spectra without relying on small angular momentum assumptions.

Contribution

It introduces a method based on Euclidean time periodicity to derive black hole area spectra, avoiding the small angular momentum approximation required in previous quasinormal mode analyses.

Findings

Area spectrum is equally spaced for both rotating and non-rotating BTZ black holes.

The method aligns with previous quasinormal mode results but does not require small angular momentum.

The approach links black hole vibrational frequencies to Euclidean time periodicity.

Abstract

The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of three dimensional black holes. We use 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 area of rotating and non-rotating BTZ black holes. It is shown that the equally spaced area spectrum takes the same form as the obtained in the literature using the quasinormal mode analysis for both metrics. Using this method, we do not need to use the small angular momentum assumption which is necessary in the quasinormal mode approach for the rotating black hole.