Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes

TL;DR

This paper uses Bohr's correspondence principle to determine that the discrete area spectrum of quantum black holes is uniformly spaced by 4 times Planck's constant times the natural logarithm of 3, aligning with thermodynamic and statistical physics principles.

Contribution

It provides a theoretical derivation of the black hole area spectrum spacing using Bohr's correspondence principle, resolving previous ambiguities.

Findings

Black hole area spectrum is discrete and uniformly spaced.

The spacing is 4ħ ln 3, consistent with thermodynamics.

Supports the quantum nature of black hole horizons.

Abstract

During the last twenty-five years evidence has been mounting that a black-hole surface area has a {\it discrete} spectrum. Moreover, it is widely believed that area eigenvalues are {\it uniformally} spaced. There is, however, no general agreement on the {\it spacing} of the levels. In this letter we use Bohr's correspondence principle to provide this missing link. We conclude that the area spacing of a black-hole is $4\hbar \ln 3$. 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}.