Black Hole (Thermodynamics) -- a Simplified Theory for Quantum Gravity Non-Specialists

TL;DR

This paper introduces a simplified semi-classical model of Schwarzschild black hole thermodynamics, linking quantum properties at the horizon to classical thermodynamic characteristics, aiming to bridge quantum gravity concepts for both specialists and non-specialists.

Contribution

It proposes a novel quasi-classical formalism connecting quantum horizon properties with black hole thermodynamics, simplifying complex relations for broader understanding.

Findings

Derived simple functional relations between black hole thermodynamics and quantum system mass.

Established a quantization condition for the horizon surface similar to Bohr's model.

Provided a framework accessible to non-specialists for understanding quantum gravity aspects.

Abstract

In this work we suggest a simplified "quasi-classical" formalism of the Schwarzschild black hole thermodynamics. We define such small quantum system at Schwarzschild black hole horizon surface whose reduced Compton wavelength equals one circumference of a great circle on the black hole horizon surface. (It is in some way similar to the Bohr orbital momentum quantization postulate for the ground state interpreted via de Broglie relation.) It admits very simple functional connections between all black hole basic thermodynamic characteristics (Unruh temperature, Hawking temperature, Bekenstein-Hawking entropy, Bekenstein entropy horizon surface quantization, evaporation time) and small quantum system mass. All this can be very interesting for the quantum gravity specialists as well as non-specialists.