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

Very recently, via the covariant form of the adiabatic invariant I = pidqi instead of I = ∫pidqi, 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 Banados—Teitelboim—Zanelli (BTZ) black hole. It is noteworthy that the adiabatic covariant action I = pidqi gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is ΔA = 8πl2P, which confirms Bekenstein's initial proposal. And the result is consistent with that already obtained by other methods.