Quantum corrections to the spectroscopy of a BTZ black hole via periodicity

Quantum corrections to the area spectrum and the entropy spectrum of a BTZ black hole are calculated by equaling the motion period of an outgoing wave coming from the quantum corrections of the semiclassical action to the period of gravitational system with respect to the Euclidean time. We find that the area spectrum and the entropy spectrum are independent of the properties of particles. Furthermore, in the presence of higher-order quantum corrections, the area spectrum is found to be corrected by inverse area terms while the entropy spectrum is found to have a universal form, $\varDelta S_{BH}=2\pi $ . Both results show that the entropy spectrum is independent of not only the BTZ black hole parameters but also the higher-order quantum corrections, which implies that the entropy spectrum is more natural than the area spectrum in quantum gravity theory.