General thermodynamic geometry approach for rotating Kerr anti-de Sitter black holes

TL;DR

This paper develops a thermodynamic geometric framework for Kerr-AdS black holes, revealing microstructural interactions and critical phenomena, and extends previous charged black hole studies to rotating cases.

Contribution

It introduces a general thermodynamic geometry approach for Kerr-AdS black holes using entropy and pressure as fluctuation coordinates, highlighting microstructure characteristics.

Findings

Near-extremal Kerr-AdS black holes exhibit dominant repulsive interactions.

Far-from-extremal Kerr-AdS black holes show dominant attractive interactions.

Critical phenomena are observed in the scalar curvature of the thermodynamic geometry.

Abstract

Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical observation of the corresponding scalar curvature, we find that, for the near-extremal Kerr-AdS black hole, the repulsive interaction dominates among its microstructure. While for far-from-extremal Kerr-AdS black hole, the attractive interaction dominates. The critical phenomenon is also observed for the scalar curvature. These results uncover the characteristic microstructure of the Kerr-AdS black hole. Such general thermodynamic geometry approach is worth generalizing to other rotating AdS black holes, and more interesting microstructure is expected to be discovered.