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

TL;DR

This paper develops a method to analyze the divergence of thermodynamic curvature scalar at critical points in black holes, revealing universal behavior across different black hole types and offering insights into their microscopic properties.

Contribution

It introduces a new approach to study the divergence of thermodynamic curvature scalar at critical points, demonstrating universality in generic black holes and applying it to dRGT massive gravity.

Findings

Universal divergence behavior of $R_N$ near critical points.

Method applicable to various black hole models.

Insights into black hole microscopic structure.

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.