Divergence behavior of thermodynamic curvature scalar at critical point in the extended phase space of generic black holes

The P-Vphase 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. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This paper investigates the P-V phase transition and critical behavior of asymptotic AdS black holes in the extended phase space, finding that four critical exponents around the critical point match those in mean field theory, and introducing a new critical exponent nu related to divergent correlation length. By studying the divergent behavior of R-N at critical point, it is discovered that this behavior is a universal property in generic black holes, with implications for the microscopic properties of black holes.