Building blocks of a black hole

TL;DR

This paper constructs a quantum model of black hole states using algebraic methods, demonstrating that the horizon area eigenvalues are exponentially degenerate, which explains the proportionality of black hole entropy to its area.

Contribution

It introduces a simple algebraic framework for black hole quantization, showing that area eigenvalues have exponential degeneracy, aligning with black hole entropy principles.

Findings

Area eigenvalues are exactly 2^n degenerate.

Black hole entropy is proportional to horizon area.

Algebraic approach generalizes harmonic oscillator algebra.

Abstract

What is the nature of the energy spectrum of a black hole ? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole states by means of a pair of "creation operators" subject to a particular simple algebra, a slight generalization of that for the harmonic oscillator. We then prove rigorously that the n-th area eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole entropy qua logarithm of the number of states for fixed horizon area comes out proportional to that area.