Thermodynamics of d-dimensional charged rotating black brane and AdS/CFT correspondence

TL;DR

This paper analyzes the thermodynamics of d-dimensional charged rotating black branes in AdS space, computing actions, verifying thermodynamic laws, and exploring stability and entropy corrections, with implications for AdS/CFT correspondence.

Contribution

It provides a detailed thermodynamic analysis of charged rotating black branes, including action computation, stability, and entropy corrections, advancing understanding in AdS/CFT context.

Findings

Logarithmic divergences vanish in the renormalization process.

The system satisfies the first law of thermodynamics.

Black branes are thermally stable with no Hawking-Page transition.

Abstract

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.