Number-phase Quantization Approach for Bohr’s Black Hole

Abstract

For black hole study, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the quantum number n of the elemental mass mi is quantized as the mass number operator and the phase difference θ is quantized as phase operator. It is proven that the number-phase quantization scheme is very useful to study systems like Bohr atom and their quantum effects. We carried out a simplified quasi-classical analysis of quantum and thermo- dynamical characteristics of a Schwarzschild’s black hole: Bekenstein-Hawking entropy, Hawking’s temperature and Bekenstein’s quantization of the surface area. In particular, it allows a simple interpretation of the black hole Bekenstein-Hawking entropy. Our analysis is analogous to the formalism of Bohr’s atomic model and, for this reason, the black hole that we consider can be called Bohr’s black hole.