Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality

Abstract

The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure P GB . We studied the critical behavior associated with P GB in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for Van der Waals system. For charged GB-AdS black holes, it is shown that there can be only one critical point in five dimensions (for black holes with either spherical or hyperbolic topologies), which also requires the electric charge to be bounded within some appropriate range; while in d > 5 dimensions, there can be up to two different critical points at the same electric charge, and the phase transition can occur only at temperatures which are not in between the two critical values.

Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

“…Thus the analogy between the charged AdS black hole and the van der Waals system becomes more complete. This analogy has been generalized to different charged black holes and rotating black holes in AdS space in the extended phase space [30][31][32][33][34][35][36][37][38][39][40][41][42].…”

Universal entropy relations: entropy formulae and entropy bound

“…These geometrical area (entropy) bounds are also studied in Gauss-Bonnet gravity [47], where the Gauss-Bonnet coupling constant should also be treated as a thermodynamical variable (see, e.g. [42,[48][49][50][51][52]). Meanwhile, area bounds are modified by the constants of theory.…”

Entropy relations and the application of black holes with the cosmological constant and Gauss–Bonnet term

“…An interesting idea is treating the cosmological constant as a thermodynamical variable (see, e.g. [31][32][33][34][35][36][37][38]). Hence, consider the first derivative of thermodynamic relations Eq.…”

“…The validity of this formula seems to work well for three-horizons black holes. We also generalize the discussion to thermodynamics for event horizon and Cauchy horizon of Gauss-Bonnet charged flat black holes, as the Gauss-Bonnet coupling constant is also considered as thermodynamical variable [35][36][37][38]43,44]). These give further clue on the crucial role that the entropy relations of multi-horizons play in black hole thermodynamics and understanding the entropy at the microscopic level.…”

“…We also obtain the Smarr relation of horizons by using the scaling discussion. For thermodynamics of all horizons, the cosmological constant is treated as a thermodynamical variable [31][32][33][34][35][36][37][38]). Especially for thermodynamics of negative horizon, it is also defined well in the negative side (r < 0).…”