Entropy spectrum of the apparent horizon of Vaidya black holes via adiabatic invariance

Abstract

The spectroscopy of the apparent horizon of Vaidya black holes is investigated via adiabatic invariance. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein [J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)]. We demonstrate that the quantization of entropy and area is a generic property of horizon, not only for stationary black holes, and the results also exit in a dynamical black hole. Our work also shows that the quantization of black hole is closely related to the tunneling formalism for deriving the Hawking effect, which is interesting.