In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant $-\frac{1}{8}$. In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity.
Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
在扩展相空间中研究了D维带电Gauss-Bonnet-AdS黑洞巨正则系综的热力学性质。我们发现，当五维球形带电Gauss-Bonnet-AdS黑洞的势固定在$0<Φ<\frac{\sqrt{3}π}{4}$范围内时，通常的小-大黑洞相变（与Van de Waals液-气系统类似）在五维球形带电Gauss-Bonnet-AdS黑洞中成立.对于其他高维拓扑带电的Gauss-Bonnet-AdS黑洞，则不存在这种相变。在Reissner-Nordstrom-AdS黑洞的极限情形下，当Gauss-Bonnet参数为零时，巨正则系综不存在临界行为.这个结果与时空维度和拓扑无关。我们还研究了五维球形带电Gauss-Bonnet-AdS黑洞临界点附近物理量的行为。
Phase Transitions, Shadows, and Microstructure of Kerr-anti-de Sitter Black Holes from Geometrothermodynamics
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
