Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole

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, $M\sim \sqrt{\mathcal{N}}{M}_p$, where $\mathcal{N}\in \mathbf{N}$. 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.

21 pages, PHYZZX macros. The counting of physical states has been corrected. Revised version to appear in Phys. Rev. D

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• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Black Holes: Classical Properties, Thermodynamics and Heuristic Quantization
• Mass Quantization of the Schwarzschild Black Hole
• Quanta of Geometry and Rotating Black Holes

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