Spectroscopy via adiabatic covariant action for the Bañados-Teitelboim-Zanelli (BTZ) black hole

Very recently, via the covariant form of the adiabatic invariant I=f p_idq_i instead of I=∫ p_idq_i, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of results. In this paper, we extend that work in a spherically symmetric spacetime to the case of a rotating Bañados-Teitelboim-Zanelli (BTZ) black hole. It is noteworthy that the adiabatic covariant action I=f p_idq_i gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is ΔA=8π l_P², which confirms the initial proposal of Bekenstein. And the result is consistent with that already obtained by other methods.