Mass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity

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dc.creatorVaz, Cenalo
dc.creatorGutti, Sashideep
dc.creatorKiefer, Claus
dc.creatorSingh, T. P.
dc.creatorWijewardhana, L. C. R.
dc.date2007-12-12
dc.date2008-02-20
dc.date.accessioned2026-07-07T11:39:22Z
dc.date.available2026-07-07T11:39:22Z
dc.descriptionIn a recent publication we developed a canonical quantization program describing the gravitational collapse of a spherical dust cloud in 2+1 dimensions with a negative cosmological constant $-Λ\equiv -l^{-2}<0$. In this paper we address the quantization of the Banados--Teitelboim--Zanelli (BTZ) black hole. We show that the mass function describing the black hole is made of two pieces, a constant non-vanishing boundary contribution and a discrete spectrum of the form $μ_n = \frac{\hbar}{l}(n+ \frac 12)$. The discrete spectrum is obtained by applying the Wheeler--DeWitt equation with a particular choice of factor ordering and interpreted as giving the energy levels of the collapsed matter shells that form the black hole. Treating a black hole microstate as a particular distribution of shells among the levels, we determine the canonical entropy of the BTZ black hole. Comparison with the Bekenstein--Hawking entropy shows that the boundary energy is related to the central charge of the Virasoro algebra that generates the asymptotic symmetry group of the three-dimensional anti-de Sitter space AdS$_3$. This gives a connection between the Wheeler--DeWitt approach and the conformal field theory approach.
dc.description15 pages, no figures. Two explanatory paragraphs have been added. This version will appear in Physical Review D
dc.identifierhttps://arxiv.org/abs/0712.1998
dc.identifierhttp://arxiv.org/abs/0712.1998
dc.identifierPhys.Rev.D77:064021,2008
dc.identifierdoi:10.1103/PhysRevD.77.064021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/199892
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectAstrophysics
dc.subjectHigh Energy Physics - Theory
dc.titleMass Spectrum and Statistical Entropy of the BTZ black hole from Canonical Quantum Gravity
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