Universal criticality of thermodynamic curvatures for charged AdS black holes

TL;DR

This paper analytically investigates the universal critical behavior of thermodynamic curvatures in charged AdS black holes, revealing consistent critical exponents and amplitudes across dimensions, providing new insights into black hole phase transitions.

Contribution

It introduces the analytical calculation of critical exponents and universal amplitudes of thermodynamic curvatures at phase transition points for charged AdS black holes, highlighting their universality.

Findings

Critical exponents for intrinsic and extrinsic curvatures are 2 and 1.

Universal amplitudes of curvature-related quantities are calculated.

Results are consistent across four and higher dimensions.

Abstract

In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes $R_Nt^2$ and $K_Nt$ are calculated with the temperature parameter $t=T/T_c-1$ where $T_c$ the critical value of the temperature. Near the critical point, we find that the critical amplitude of $R_Nt^2$ and $K_Nt$ is $-\frac{1}{2}$ when $t\rightarrow0^+$, whereas $R_Nt^2\approx -\frac{1}{8}$ and $K_Nt\approx-\frac{1}{4}$ in the limit $t\rightarrow0^-$. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.