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The $P$-$V$ phase transition and critical behavior in the extended phasespace of asymptotic Anti-de Sitter (AdS) black holes have been widelyinvestigated, in which four critical exponents around critical point are foundto be consistent with values in the mean field theory. Recently, anothercritical exponent $\nu$ related to divergent correlation length at criticalpoint is proposed by using thermodynamic curvature scalar $R_N$ in the chargedAdS black hole. In this paper, we develop a method to investigate the divergentbehavior of $R_N$ at critical point, and find that the divergent behavior of$R_N$ around the critical point expresses a universal property in generic blackholes. We further directly apply this method to investigate black holes in deRham-Gabadadze-Tolley (dRGT) massive gravity to check this universality. Thoseresults shed new lights on the microscopic properties of black holes.

Divergence Behavior of Thermodynamic Curvature Scalar at Critical Point in the Extended Phase Space of Generic Black Holes