Gravitation, the Quantum, and Bohr's Correspondence Principle

TL;DR

This paper proposes that black-hole surface area is quantized with a fundamental unit of 4ħln3, linking quantum gravity, thermodynamics, and Bohr's correspondence principle to support a quantum theory of black holes.

Contribution

It introduces a specific quantization of black hole surface area using Bohr's correspondence principle, resolving the level spacing ambiguity in quantum gravity models.

Findings

Black-hole surface area is quantized with a fundamental unit of 4ħln3.

The quantization is consistent with thermodynamic and statistical physics principles.

Provides a theoretical basis linking quantum gravity and classical physics via Bohr's principle.

Abstract

The black hole combines in some sense both the ``hydrogen atom'' and the ``black-body radiation'' problems of quantum gravity. This analogy suggests that black-hole quantization may be the key to a quantum theory of gravity. During the last twenty-five years evidence has been mounting that black-hole surface area is indeed {\it quantized}, with {\it uniformally} spaced area eigenvalues. There is, however, no general agreement on the {\it spacing} of the levels. In this essay we use Bohr's correspondence principle to provide this missing link. We conclude that the fundamental area unit is $4\hbar\ln3$. This is the unique spacing consistent both with the area-entropy {\it thermodynamic} relation for black holes, with Boltzmann-Einstein formula in {\it statistical physics} and with {\it Bohr's correspondence principle}.