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Title: Inside the BTZ black hole

Abstract

We consider a static circularly symmetric solution of three-dimensional Einstein equations with a negative cosmological constant (the BTZ black hole). The case of the zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. We prove that the maximally extended BTZ solution with the zero cosmological constant coincides with flat three-dimensional Minkowskian space-time without any singularities and horizons. The Euclidean version of this solution is shown to have a physical interpretation in the geometric theory of defects in solids describing combined wedge and screw dislocations.

Authors:
;  [1];  [2]
  1. Departamento de Fisica, Universidade Federal de Juiz de Fora, Juiz de Fora CEP 36036-330, MG (Brazil)
  2. (Russian Federation)
Publication Date:
OSTI Identifier:
20935223
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; COSMOLOGICAL CONSTANT; EINSTEIN FIELD EQUATIONS; EUCLIDEAN SPACE; MATHEMATICAL SOLUTIONS; MINKOWSKI SPACE; SCREW DISLOCATIONS; SINGULARITY; SPACE-TIME; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Berredo-Peixoto, G. de, Katanaev, M. O., and Steklov Mathematical Institute, Gubkin Street 8, Moscow, 119991. Inside the BTZ black hole. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.024004.
Berredo-Peixoto, G. de, Katanaev, M. O., & Steklov Mathematical Institute, Gubkin Street 8, Moscow, 119991. Inside the BTZ black hole. United States. doi:10.1103/PHYSREVD.75.024004.
Berredo-Peixoto, G. de, Katanaev, M. O., and Steklov Mathematical Institute, Gubkin Street 8, Moscow, 119991. Mon . "Inside the BTZ black hole". United States. doi:10.1103/PHYSREVD.75.024004.
@article{osti_20935223,
title = {Inside the BTZ black hole},
author = {Berredo-Peixoto, G. de and Katanaev, M. O. and Steklov Mathematical Institute, Gubkin Street 8, Moscow, 119991},
abstractNote = {We consider a static circularly symmetric solution of three-dimensional Einstein equations with a negative cosmological constant (the BTZ black hole). The case of the zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. We prove that the maximally extended BTZ solution with the zero cosmological constant coincides with flat three-dimensional Minkowskian space-time without any singularities and horizons. The Euclidean version of this solution is shown to have a physical interpretation in the geometric theory of defects in solids describing combined wedge and screw dislocations.},
doi = {10.1103/PHYSREVD.75.024004},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which is manifestly non-negative, such that the second law of thermodynamics is satisfied. I show that the new thermodynamical entropy agrees perfectly with the statistical entropy for all the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literature. The agreement with both the higher curvature and gravitational Chern-Simons terms is possible becausemore » of an appropriate balancing of them, though it is not a trivial matter because of a conflict in the appropriate Hilbert space for a well-defined conformal field theory for each term.« less
  • 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 shellsmore » 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.« less
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  • We study the properties of the space of thermodynamic equilibrium states of the Banados-Teitelboim-Zanelli (BTZ) black hole in (2+1) gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a two-dimensional thermodynamic metric whose curvature is nonvanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea thatmore » thermodynamic curvature is a measure of thermodynamic interaction.« less
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