The phase transition and thermodynamic geometry of a 4-dimensional AdS topological charged black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity have been studied. After introducing a normalized thermodynamic scalar curvature, it is speculated that its value is related to the interaction between the underlying black hole molecules if the black hole molecules exist. We show that there does exist a crucial parameter given in terms of the topology, charge, and massive parameters of the black hole, which characterizes the thermodynamic properties of the black hole. It is found that when the parameter is positive, the singlet large black hole phase does not exist for sufficient low temperature and there is a weak repulsive interaction dominating for the small black hole which is similar to the Reissner–Nordström AdS black hole; when the parameter is negative, an additional phase region describing large black holes also implies a dominant repulsive interaction. These constitute the distinguishable features of dRGT massive topological black hole from those of the Reissner–Nordström AdS black hole as well as the Van der Waals fluid system.

已经研究了 de Rham、Gabadadze 和 Tolley (dRGT) 大质量引力中 4 维 AdS 拓扑带电黑洞的相变和热力学几何形状。引入归一化的热力学标量曲率后，推测如果存在黑洞分子，其值与底层黑洞分子之间的相互作用有关。我们表明确实存在一个关于黑洞拓扑、电荷和质量参数的关键参数，它表征了黑洞的热力学特性。发现当参数为正时，在足够低的温度下不存在单线态大黑洞相，并且存在弱排斥相互作用主导小黑洞，类似于Reissner-Nordström AdS黑洞；当参数为负时，描述大黑洞的附加相位区域也意味着主要的排斥相互作用。这些构成了 dRGT 大质量拓扑黑洞与 Reissner-Nordström AdS 黑洞以及范德瓦尔斯流体系统的区别特征。