Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole

TL;DR

This paper applies canonical quantization to Schwarzschild black holes, revealing a spectrum consistent with the statistical bootstrap model and deriving the black hole's entropy by microstate counting.

Contribution

It introduces a quantization framework that models black holes as oscillators and connects their microstates to the Bekenstein mass spectrum.

Findings

Black hole states resemble a collection of oscillators.

Derived Bekenstein mass spectrum from quantized states.

Calculated black hole entropy via microstate enumeration.

Abstract

The canonical quantization of a Schwarzschild black hole yields a picture of the black hole that is shown to be equivalent to a collection of oscillators whose density of levels is commensurate with that of the statistical bootstrap model. Energy eigenstates of definite parity exhibit the Bekenstein mass spectrum, $M \sim \sqrt{\cal N} M_p$, where ${\cal N} \in {\bf N}$. From the microcanonical ensemble, we derive the statistical entropy of the black hole by explicitly counting the microstates corresponding to a macrostate of fixed total energy.