Thermodynamics curvature in phase transitions for AdS black hole

TL;DR

This paper explores the behavior of thermodynamic curvature during phase transitions of AdS black holes, revealing universal patterns and differences in high-dimensional limits that deepen understanding of black hole thermodynamics.

Contribution

It demonstrates that thermodynamic curvature behaves similarly in Hawking-Page and second-order phase transitions, with universal ratios approaching the natural constant in large dimensions.

Findings

Thermodynamic curvature is a power function of transition temperature.

The ratio of curvatures tends to the natural constant as dimensions increase.

Universal behavior links different phase transitions in high-dimensional black holes.

Abstract

We investigate the thermodynamic curvature in the Hawking-Page phase transition and the second-order phase transition of the AdS black hole. It is shown that the thermodynamic curvature has the same behavior in these two different phase transitions. Specifically, the thermodynamic curvature in the Hawking-Page phase transition is the power function of the Hawking-Page phase transition temperature with exponent related to the spacetime dimension, or is invariably proportional to the reciprocal of the Hawking-Page phase transition entropy. For the thermodynamic curvature in the second-order phase transition, the conclusion is similar. The more enlightening result is that the ratio of thermodynamic curvatures along the two different phase transitions tends to the natural constant in the limit that the number of spacetime dimensions is infinite. The universal and novel result provides an essential difference between the Hawking-Page phase transition and the second-order phase transition of the AdS black hole in the large dimension paradigm.