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Title: Hamiltonian thermodynamics of three-dimensional dilatonic black holes

Abstract

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemblemore » is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

Authors:
;  [1]
  1. Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
Publication Date:
OSTI Identifier:
21250494
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 78; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.78.044010; (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:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BIFURCATION; BLACK HOLES; CANONICAL DIMENSION; COSMOLOGICAL CONSTANT; CYLINDRICAL CONFIGURATION; DE SITTER GROUP; ENTROPY; EVOLUTION; FOUR-DIMENSIONAL CALCULATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; HAMILTONIANS; MASS; PARTITION FUNCTIONS; QUANTUM GRAVITY; QUANTUM OPERATORS; SCHROEDINGER EQUATION; THERMODYNAMICS; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Dias, Goncalo A. S., and Lemos, Jose P. S. Hamiltonian thermodynamics of three-dimensional dilatonic black holes. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.78.044010.
Dias, Goncalo A. S., & Lemos, Jose P. S. Hamiltonian thermodynamics of three-dimensional dilatonic black holes. United States. doi:10.1103/PHYSREVD.78.044010.
Dias, Goncalo A. S., and Lemos, Jose P. S. Fri . "Hamiltonian thermodynamics of three-dimensional dilatonic black holes". United States. doi:10.1103/PHYSREVD.78.044010.
@article{osti_21250494,
title = {Hamiltonian thermodynamics of three-dimensional dilatonic black holes},
author = {Dias, Goncalo A. S. and Lemos, Jose P. S.},
abstractNote = {The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.},
doi = {10.1103/PHYSREVD.78.044010},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 4,
volume = 78,
place = {United States},
year = {2008},
month = {8}
}