Area spectra of BTZ black holes via periodicity

Abstract

Motivated by the recent work that the periodicity of a black hole is responsible for the area spectrum, 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 study area spectra of a non-rotating BTZ black hole and a rotating BTZ black hole. It is found that the area spectra and entropy spectra for both space times are equally spaced. In addition, we find that though the entropy spectra of the 3-dimensional BTZ black holes take the same form as those of the 4-dimensional black holes, the area spectra depend on the dimension of space times. Our result confirms that the entropy spectrum of a black hole is more fundamental than the area spectrum.