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Paper IPM / P / 6941  


Abstract:  
We compute the Euclidean actions of a ddimensional charged rotating black brane both in the canonical and the grandcanonical 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 Smarrtype 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 grandcanonical 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 HawkingPage 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.
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