Sommerfeld's quantum condition of action and the spectra of Schwarzschild black hole

TL;DR

This paper applies Sommerfeld's quantum condition to Schwarzschild black holes, deriving their quantum spectra and suggesting that Hawking evaporation halts at the ground state, offering a quasi-classical quantum gravity perspective.

Contribution

It introduces a quasi-classical approach to black hole spectra using Sommerfeld's quantization, connecting early quantum mechanics concepts to black hole physics.

Findings

Quantum of area and entropy derived for Schwarzschild black holes

Hawking evaporation stops at the black hole's ground state

Provides a quasi-classical quantum gravity framework

Abstract

If the situation of quantum gravity nowadays is nearly the same as that of the quantum mechanics in it's early time of Bohr and Sommerfeld, then a first step study of the quantum gravity from Sommerfeld's quantum condition of action might be helpful. In this short paper the spectra of Schwarzschild black hole(SBH) in quasi-classical approach of quantum mechanics is given. We find the quantum of area, the quantum of entropy and the Hawking evaporation will cease as the black hole reaches its ground state.