Periodicity and area spectrum of the three dimensional BTZ black hole

Abstract

Very recently, a new scheme to quantize the horizon area of a black hole has been proposed by Zeng and Liu et al. In this paper, we further apply the analysis to investigate area spectrum of three dimensional BTZ black hole with the cosmological constant ${\Lambda=-1/l^{2}}$ . The results show that the area spectrum and entropy spectrum are independent of the cosmological constant. The area spectrum of the black hole is ${\Delta A=8\pi l_{P}^{2}}$ , which confirms the initial proposal of Bekenstein that the area spectrum is independent of the black hole parameters and the spacing is ${8\pi l_{P}^{2}}$ . This result also confirms the speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization. In addition, for the rotating and non-rotating BTZ black holes, we obtain the same entropy spectrum ${\triangle S=2\pi}$ , which is consistent with the result for other black holes. This implies that the entropy spectrum is more fundamental than the area spectrum.