Bekenstein-Smarr formula and quantization of Kerr black holes

Abstract

By solving the zero surface equation and studying the black holes law, we derive the equivalent Bekenstein-Smarr formula for Kerr black holes. With the reduced phase space method and canonical transformation, we establish the quantum mechanical model for Kerr black hole which is a standard two-mode simple harmonic oscillator model. With the help of this model, we further derive the spectra of the event horizon area and corresponding eigen wave functions for the Kerr black holes, which are proved that the area of a black hole event horizon is quantized.