Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-12-11
Phys.Rev.D67:084006,2003
Physics
High Energy Physics
High Energy Physics - Theory
REVTEX4, 15 pages, 1 figure
Scientific paper
10.1103/PhysRevD.67.084006
We compute the Euclidean actions of a $d$-dimensional charged rotating black brane both in the canonical and the grand-canonical ensemble through the use of the counterterms renormalization method, and show that the logarithmic divergencies associated with the Weyl anomalies and matter field vanish. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta, and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Using the conserved quantities and the Euclidean actions, we calculate the thermodynamics potentials of the system in terms of the temperature, angular velocities, and electric potential both in the canonical and grand-canonical ensembles. We also perform a stability analysis in these two ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for a black object with zero curvature horizon. Finally, we obtain the logarithmic correction of the entropy due to the thermal fluctuation around the equilibrium.
Dehghani M. H.
Khodam-Mohammadi A.
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