The Case for Discrete Energy Levels of a Black Hole

TL;DR

This paper proposes a simple algebraic method for black hole quantization, predicting a discrete, evenly spaced area spectrum with degeneracies, linking quantum properties to classical symmetries and entropy.

Contribution

It introduces a novel algebraic approach to black hole quantization based on symmetry, predicting a universal discrete area spectrum with specific degeneracies.

Findings

Predicts a uniformly spaced area spectrum for all black hole charges and angular momenta.

Establishes a relationship between eigenvalue degeneracy and black hole entropy.

Provides a method to determine the interval between area eigenvalues.

Abstract

The adiabatic invariant nature of black hole horizon area in classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which starts from very elementary assumptions, and proceeds by exploiting symmetry. It predicts a uniformly spaced area spectrum for all charges and angular momenta. Area eigenvalues are degenerate; correspondence with black hole entropy then dictates a precise value for the interval between eigenvalues.