Remarks on Spectroscopy via Adiabatic Invariance from the Kerr Black Hole

Abstract

By imposing Bohn-Sommerfeld quantization rule and the laws of black hole thermodynamics to the modified adiabatic covariant action, the spectroscopy of the Kerr black hole is obtained in different coordinate frames. The result shows that the area spectrum is equidistant spacing, and the Bekenstein’s original result \({\Delta } A=8\pi {l_{p}^{2}}\) is also recovered. Especially, in contrast to the quasinormal mode method, in our analysis there is no need to impose the small angular momentum limit for the Kerr black hole spectroscopy.