A Simple, Approximate Method for Analysis of Kerr-Newman Black Hole Dynamics and Thermodynamics

TL;DR

This paper introduces a simplified, approximate approach to analyze Kerr-Newman black hole dynamics and thermodynamics by linking quantum states to black hole properties, providing new insights into entropy, temperature, and Hawking radiation.

Contribution

It presents a novel, simplified method connecting quantum states with black hole characteristics, offering new perspectives on black hole thermodynamics and radiation.

Findings

Black hole entropy relates to quantum ground state degeneracy.

Black hole temperature corresponds to classical gravitational potential energy.

The model offers a qualitative understanding of Hawking radiation.

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 such stable (stationary) dynamical situations determined by condition that 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 quant of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the quotient of the sum of static part and rotation part of mass of black hole on the one hand and 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 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 ground mass quantum state is significantly degenerate while all 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.