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

Journal Article · Sat Mar 15 00:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.064021· OSTI ID:21249839

Vaz, Cenalo; Wijewardhana, L C. R. ^[1]; Gutti, Sashideep; Singh, T P ^[2]; Kiefer, Claus ^[3]

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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)

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.

• OSTI ID: 21249839
• Journal Information: Physical Review. D, Particles Fields, Vol. 77, Issue 6; Other Information: DOI: 10.1103/PhysRevD.77.064021; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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