The Quantum Formulation of Black Hole Area Spectrum and Entropy Spectrum

In this paper, the area spectrum of this static BTZ black hole in different cases (rotating, non-rotating, and extreme) is investigated. The final results show that the spectral formulation is 2πnℏ when this black hole is non-rotating. For the black hole in other two different cases, its spectrum is angular momentum-dependent. Unexpectedly, their area spectra are both equally spaced. What is more, the entropy spectrum is also calculated via the method put forward by Chen et al. However, it is demonstrated that the well known area-entropy law is greatly changed. Above all, the entropy spectrum of this non-rotating BTZ black hole is also equally spaced.