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

Abstract

The thermodynamic phase space of GaussBonnet (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 the 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.

Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

“…In these circumstances, the black hole mass known as an internal energy is replaced by enthalpy. Recently, the critical behavior of charged AdS black holes such as Reissner-Nordstrom-AdS and Kerr-Newman-AdS black holes has been investigated in the extended phase space (while the cosmological constant Λ is included as a thermodynamic variable) and in the canonical ensemble [24,25,42,43]. The critical behaviors are analogous to the liquid-gas phase transition in the Van der Waals fluid.…”

Entropy relations and bounds of horizons in modified gravity

“…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.…”

Black holes and Boyle's law — The thermodynamics of the cosmological constant

“…For a charged black hole with a spherical event horizon there are critical points, associated with large black/small black hole phase transitions, with mean field exponents [122]- [124].…”

“…For D = 5 this can happen even when the black hole is electrically neutral but for D ≥ 6 there must be a non-zero charge [122]. In [125] it was found that, when the potential Φ is held fixed rather than the electric charge, the critical point persists only for D = 5.…”