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Title: Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity

Abstract

In 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 -{lambda}{identical_to}-l{sup -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 nonvanishing boundary contribution and a discrete spectrum of the form {mu}{sub n}=(({Dirac_h}/2{pi})/l)(n+(1/2)). 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{sub 3}. This gives a connection between the Wheeler-DeWitt approach and the conformal field theory approach.

Authors:
;  [1]; ;  [2];  [3]
  1. RWC and Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221-0011 (United States)
  2. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 (India)
  3. Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Koeln (Germany)
Publication Date:
OSTI Identifier:
21249839
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 77; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.77.064021; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASYMPTOTIC SOLUTIONS; BLACK HOLES; COMPARATIVE EVALUATIONS; CONFORMAL INVARIANCE; COSMIC DUST; COSMOLOGICAL CONSTANT; DE SITTER GROUP; DISTRIBUTION; ENERGY LEVELS; ENTROPY; EQUATIONS; GRAVITATIONAL COLLAPSE; MASS; MASS SPECTRA; QUANTIZATION; QUANTUM GRAVITY; SPHERICAL CONFIGURATION; SYMMETRY GROUPS; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Vaz, Cenalo, Wijewardhana, L C. R., Gutti, Sashideep, Singh, T P, and Kiefer, Claus. Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.77.064021.
Vaz, Cenalo, Wijewardhana, L C. R., Gutti, Sashideep, Singh, T P, & Kiefer, Claus. Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity. United States. doi:10.1103/PHYSREVD.77.064021.
Vaz, Cenalo, Wijewardhana, L C. R., Gutti, Sashideep, Singh, T P, and Kiefer, Claus. Sat . "Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity". United States. doi:10.1103/PHYSREVD.77.064021.
@article{osti_21249839,
title = {Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity},
author = {Vaz, Cenalo and Wijewardhana, L C. R. and Gutti, Sashideep and Singh, T P and Kiefer, Claus},
abstractNote = {In 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 -{lambda}{identical_to}-l{sup -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 nonvanishing boundary contribution and a discrete spectrum of the form {mu}{sub n}=(({Dirac_h}/2{pi})/l)(n+(1/2)). 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{sub 3}. This gives a connection between the Wheeler-DeWitt approach and the conformal field theory approach.},
doi = {10.1103/PHYSREVD.77.064021},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 77,
place = {United States},
year = {2008},
month = {3}
}