Hamiltonian thermodynamics of threedimensional dilatonic black holes
Abstract
The action for a class of threedimensional dilatongravity theories with a negative cosmological constant can be recast in a BransDicke 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 fourdimensional 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 CarterPenrose diagram, with the bifurcation 1sphere as the left boundary, and antide 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 »
 Authors:

 Centro Multidisciplinar de AstrofisicaCENTRA, Departamento de Fisica, Instituto Superior TecnicoIST, Universidade Tecnica de LisboaUTL, Avenida Rovisco Pais 1, 1049001 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 05562821
 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; FOURDIMENSIONAL CALCULATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; HAMILTONIANS; MASS; PARTITION FUNCTIONS; QUANTUM GRAVITY; QUANTUM OPERATORS; SCHROEDINGER EQUATION; THERMODYNAMICS; THREEDIMENSIONAL CALCULATIONS
Citation Formats
Dias, Goncalo A. S., and Lemos, Jose P. S. Hamiltonian thermodynamics of threedimensional 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 threedimensional dilatonic black holes. United States. doi:10.1103/PHYSREVD.78.044010.
Dias, Goncalo A. S., and Lemos, Jose P. S. Fri .
"Hamiltonian thermodynamics of threedimensional dilatonic black holes". United States. doi:10.1103/PHYSREVD.78.044010.
@article{osti_21250494,
title = {Hamiltonian thermodynamics of threedimensional dilatonic black holes},
author = {Dias, Goncalo A. S. and Lemos, Jose P. S.},
abstractNote = {The action for a class of threedimensional dilatongravity theories with a negative cosmological constant can be recast in a BransDicke 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 fourdimensional 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 CarterPenrose diagram, with the bifurcation 1sphere as the left boundary, and antide 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 = {05562821},
number = 4,
volume = 78,
place = {United States},
year = {2008},
month = {8}
}