Thermodynamics of rotating solutions in Gauss-Bonnet-Maxwell gravity and the counterterm method

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. * email address: mhd@shirazu.ac.ir † email address: bordbar@physics.susc.ac.ir

Quintessence background for 5D Einstein–Gauss–Bonnet black holes

“…Since its inception, steadily attention has been given to black hole solutions, including their formation, stability, and thermodynamics. The spherically symmetric static black hole solution for the Einstein-Gauss-Bonnet theory was first obtained by Boulware and Deser [3][4][5], and later several authors explored exact black hole solutions and their thermodynamical properties [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The generalization of the Boulware-Desser solution has been obtained with a source as a cloud of strings, in Einstein-Gauss-Bonnet gravity [24,25], and also in Lovelock gravity [26][27][28].…”

Thermodynamics of Third Order Lovelock—Born—Infeld Black Holes

“…(12). The Hawking temperature of black holes on the outer horizon radius r + can be easily obtained by [30] T + = f ′ (r + ) 4π…”

“…So far, the exact static and spherically symmetric black hole solutions have been investigated in [7], thermodynamics of black holes in [7][8][9][10] in third order Lovelock gravity. In addition, some rotating black branes [11][12][13] and slowly rotating black holes [14][15][16][17] have been discussed in the second (Gauss-Bonnet) and third order Lovelock gravity.…”

Topological black holes in Gauss–Bonnet gravity with conformally invariant Maxwell source

“…For charged real solution one needs a transformation to make them real [7,29]. In the other word, f (ρ) is real only in the range r 0 ρ < ∞, where r 0 is the largest real root of the following equation…”

“…For asymptotically AdS of our solutions with flat boundary, R abcd (γ) = 0, the finite action, I G + I ct , reduce to [26,29] …”