Thermodynamics of Gauss–Bonnet black holes revisited

Abstract

We investigate the Gauss-Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss-Bonnet coupling c and mass M , comparing with those of the Born-Infeld-AdS (BIAdS), Reissner-Norström-AdS black holes (RNAdS), SchwarzschildAdS (SAdS), and BTZ black holes. For c < 0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy because the entropy does not satisfy the area-law. On the other hand, for c > 0, we find the BIAdS-like black hole, showing that the coupling c plays the role of pseudo-charge. Importantly, we could not obtain the SAdS in the limits of c → 0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasinormal modes may take analytic expressions.

Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter black hole with higher derivative gauge corrections

“…This differs from the situation in d = 4 spacetime dimensions [27], shown in figure 19(a), where one of the metastable modes is always thermally unfavored with respect to the thermal anti-de Sitter vacuum. It may be somewhat alarming that the effect occurs for c < 0; however, from a purely effective field theory point of view, we must take these effects seriously, unless there is evidence that this is an unphysical region of parameter space (see [52,53] for a relevant discussion for the neutral case). It would be very interesting to understand the dual field theory interpretation of these metastable modes given that the phase transition occurs between two states in the deconfined phase.…”

Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes

“…Among the gravity theories with higher derivative curvature terms, the Gauss-Bonnet (GB) gravity has some special features and gives rise to some interesting effects on the thermodynamics of black holes in AdS space [34][35][36][37][38][39][40][41][42]. The phase structure of a GB-AdS black hole was briefly studied in [34,43].…”

Phase transition of AdS–Schwarzschild black hole and gauge theory dual in the presence of external string cloud

“…Subsequently, several other extensions of this work appeared. These includes the consideration of the R-charges [5][6][7], addition of the Gauss-Bonnet [8][9][10][11][12][13][14] corrections or the Born-Infeld [15][16][17][18][19] term ( separately and combination [20][21][22][23] of these terms in the AdS-Schwarzschild black hole) into the action.…”