Area and entropy spectra of black holes via an adiabatic invariant

By considering an adiabatic invariant for black holes, the area and entropy spectra of static spherically-symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.