Microstructure of charged AdS black hole via $P-V$ criticality

TL;DR

This paper introduces a new thermodynamic curvature based on adiabatic compressibility to study the microstructure of charged AdS black holes, revealing dominant repulsive interactions in small black holes and divergence behaviors at extremal and critical points.

Contribution

It proposes a novel thermodynamic curvature measure for black holes and analyzes their microstructure during phase transitions, highlighting interaction types and divergence behaviors.

Findings

Strong repulsive interactions in near extremal small black holes

Thermodynamic curvature diverges to positive infinity for extremal black holes

Curvature diverges to negative infinity at the critical point

Abstract

We suggest a new thermodynamic curvature, constructed via adiabatic compressibility, for examining the internal microstructure of charged black holes in an anti-de Sitter (AdS) background. We analyze the microscopic properties of small-large phase transition of black holes with pressure and volume as the fluctuation variables. We observe that strong repulsive interactions dominate among the micro-structures of near extremal small black holes, and the thermodynamic curvature diverges to positive infinity for the extremal black holes. At the critical point, however, thermodynamic curvature diverges to negative infinity.