A Bohr's Semiclassical Model of the Black Hole Thermodynamics

TL;DR

This paper introduces a semiclassical model for black hole thermodynamics inspired by Bohr's atomic model, providing estimates for entropy, temperature, and area quantization that align with established results and offering insights into black hole radiation and evaporation.

Contribution

It presents a novel semiclassical approach based on Bohr-like quantization to evaluate black hole thermodynamics, aligning with Hawking's predictions and confirming Bekenstein's energy quantization.

Findings

Agreement with Hawking's evaporation time estimates

Confirmation of Bekenstein's entropy and area quantization

Conceptual analogy between black hole radiation and Bohr's photon emission

Abstract

We propose a simple procedure for evaluating the main thermodynamical attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking's temperature and Bekenstein's quantization of the surface area. We make use of the condition that the circumference of a great circle on the black hole horizon contains finite number of the corresponding reduced Compton's wavelength. It is essentially analogous to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie's relation. We present black hole radiation in the form conceptually analogous to Bohr's postulate on the photon emission by discrete quantum jump of the electron within the Old quantum theory. It enables us, in accordance with Heisenberg's uncertainty relation and Bohr's correspondence principle, to make a rough estimate of the time interval for black hole evaporation, which turns out very close to time interval predicted by the standard Hawking's theory. Our calculations confirm Bekenstein's semiclassical result for the energy quantization, in variance with Frasca's (2005) calculations. Finally we speculate about the possible source-energy distribution within the black hole horizon.