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

Abstract

The $P$-$V$ phase transition and critical behavior in the extended phase space of asymptotic Anti-de Sitter (AdS) black holes have been widely investigated, in which four critical exponents around critical point are found to be consistent with values in the mean field theory. Recently, another critical exponent $\nu$ related to divergent correlation length at critical point is proposed by using thermodynamic curvature scalar $R_N$ in the charged AdS black hole. In this paper, we develop a method to investigate the divergent behavior 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 black holes. We further directly apply this method to investigate black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity to check this universality. Those results shed new lights on the microscopic properties of black holes.

10 pages, no figure, version accepted by PLB

References in corpus (7)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• P-V criticality in the extended phase space of black holes in massive gravity
• Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• Van der Waals criticality in AdS black holes: a phenomenological study
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• The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss-Bonnet gravity: from the critical point to the triple point
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP
• Cooling-Heating Properties of the FRW Universe in Gravity with a Generalized Conformal Scalar Field
• General thermodynamic geometry approach for rotating Kerr anti-de Sitter black holes