Canonical Quantization and the Statistical Entropy of the Schwarzschild Black Hole

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.61.064017

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.

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