A simple, approximate method for analysis of Kerr-Newman black hole dynamics and thermodynamics

Abstract

In this work we present a simple approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction, we consider only the stable (stationary) dynamical situations determined by condition that the black hole (outer) horizon 'circumference' holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing the quantum of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the ratio of the sum of static part and rotation part of the mass of black hole on one hand, and the ground mass of small quantum system on the other hand. Also we show that Kerr-Newman black hole temperature represents the negative value of the classical potential energy of gravitational interaction between a part of black hole with reduced mass and a small quantum system in the ground mass quantum state. Finally, we suggest a bosonic great canonical distribution of the statistical ensemble of given small quantum systems in the thermodynamical equilibrium with (macroscopic) black hole as thermal reservoir. We suggest that, practically, only the ground mass quantum state is significantly degenerate while all the other, excited mass quantum states, are non-degenerate. Kerr-Newman black hole entropy is practically equivalent to the ground mass quantum state degeneration. Given statistical distribution admits a rough (qualitative) but simple modeling of Hawking radiation of the black hole too.