Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method

TL;DR

This paper derives and analyzes charged rotating black hole solutions in Gauss-Bonnet gravity, demonstrating their thermodynamic properties, stability, and the consistency of different computational methods.

Contribution

It provides explicit charged rotating solutions in Gauss-Bonnet gravity and confirms their thermodynamic consistency using the counterterm method.

Findings

Solutions have two horizons, extremal, or naked singularities depending on parameters.

Finite action and thermodynamic quantities match across methods.

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

Abstract

By a suitable transformation, we present the $(n+1)$-dimensional charged rotating solutions of Gauss-Bonnet gravity with a complete set of allowed rotation parameters which are real in the whole spacetime. We show that these charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. Using the surface terms that make the action well-defined for Gauss-Bonnet gravity and the counterterm method for eliminating the divergences in action, we compute finite action of the solutions. We compute the conserved and thermodynamical quantities through the use of free energy and the counterterm method, and find that the two methods give the same results. We also find that these quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.