Hamiltonian thermodynamics of d-dimensional (d{>=}4) Reissner-Nordstroem-anti-de Sitter black holes with spherical, planar, and hyperbolic topology

Journal Article · Sun Feb 15 04:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.044013· OSTI ID:21266318

Dias, Goncalo A. S.; Lemos, Jose P. S. ^[1]

---

1. Centro Multidisciplinar de Astrofisica-ENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

The Hamiltonian thermodynamics formalism is applied to the general d-dimensional Reissner-Nordstroem-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology. After writing its action and performing a Legendre transformation, surface terms are added in order to guarantee a well-defined variational principle with which to obtain sensible equations of motion, and also to allow later on the thermodynamical analysis. Then a Kuchar canonical transformation is done, which changes from the metric canonical coordinates to the physical parameters coordinates. Again, a well-defined variational principle is guaranteed through boundary terms. These terms influence the falloff conditions of the variables and at the same time the form of the new Lagrange multipliers. Reduction to the true degrees of freedom is performed, which are the conserved mass and charge of the black hole. Upon quantization a Lorentzian partition function Z is written for the grand canonical ensemble, where the temperature T and the electric potential {phi} are fixed at infinity. After imposing Euclidean boundary conditions on the partition function, the respective effective action I{sub *}, and thus the thermodynamical partition function, is determined for any dimension d and topology k. This is a quite general action. Several previous results can be then condensed in our single general formula for the effective action I{sub *}. Phase transitions are studied for the spherical case, and it is shown that all the other topologies have no phase transitions. A parallel with the Bose-Einstein condensation can be established. Finally, the expected values of energy, charge, and entropy are determined for the black hole solution.

• OSTI ID: 21266318
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 79; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BLACK HOLES
BOSE-EINSTEIN CONDENSATION
BOUNDARY CONDITIONS
CANONICAL DIMENSION
CANONICAL TRANSFORMATIONS
COORDINATES
DE SITTER GROUP
DEGREES OF FREEDOM
ENTROPY
EQUATIONS OF MOTION
EUCLIDEAN SPACE
HAMILTONIANS
MATHEMATICAL SOLUTIONS
PARTITION FUNCTIONS
QUANTIZATION
SIMULATION
SPHERICAL CONFIGURATION
THERMODYNAMICS
VARIATIONAL METHODS