Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space

Abstract

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the fivedimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity.

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss-Bonnet gravity: from the critical point to the triple point

“…However, in other dimensions of spacetime, the case behaves quite differently. For the four-dimensional case, we found that the small-large black hole phase transition exists both in the canonical and grand canonical ensembles [43]. The corresponding geometry suggests that the repulsive interaction dominates for the high temperature small black holes, quite similar to the charged case in Einstein-Maxwell gravity.…”

“…In particular, the critical phenomena are observed for the normalized curvature scalar reflecting a universal property of the Ruppeiner geometry. Such study has also been extended to other black hole systems and much more interesting results were obtained [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions

“…which are just the four-dimensional charged Gauss-Bonnet black holes in AdS space [52]. If α → 0, we can recover the four-dimensional AdS Reissner-Nordström black hole.…”

“…Considering the comments and criticisms on the original version of the 4D Einstein-Gauss-Bonnet gravity [39][40][41][42][43][44], some researchers proposed the "regularized" versions of the 4D Einstein-Gauss-Bonnet gravity [45][46][47][48] and the consistent theory of the D → 4 Einstein-Gauss-Bonnet gravity [49]. In particular, using the consistent D → 4 Einstein-Gauss-Bonnet gravity, the authors of [50] obtained the 4D Gauss-Bonnet-AdS black hole solution, which was proved out to be the solution obtained via the scalar-tensor theories with the Gauss-Bonnet term [45,46] as well as the naive D → 4 limit of the higher-dimensional theory [51][52][53]. Thus, the (2 + 1)-dimensional Gauss-Bonnet superconductors in the probe limit were constructed in Ref.…”

General thermodynamic geometry approach for rotating Kerr anti-de Sitter black holes

“…The approach has also been generalized to other black hole backgrounds [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. For the neutral AdS black hole, we constructed its Ruppeiner geometry, and found that there is only the attractive interaction for arbitrary spacetime dimension.…”