Thermogeometric phase transition in a unified framework

TL;DR

This paper uses geothermodynamics to analyze black hole phase transitions, showing that curvature scalar singularities correspond to specific heat divergences universally, and clarifying the nature of different phase transition types.

Contribution

It provides a metric-independent framework to identify black hole phase transitions through geometric singularities, unifying previous case-by-case analyses.

Findings

Curvature scalar diverges at specific heat divergence for all black holes.

Inverse specific heat divergence corresponds to metric singularity, not curvature scalar.

GTD indicates specific heat singularity as the true phase transition indicator.

Abstract

Using geomterothermodynamics (GTD), we investigate the phase transition of black hole in a metric independent way. We show that for any black hole, curvature scalar (of equilibrium state space geometry) is singular at the point where specific heat diverges. Previously such a result could only be shown by taking specific examples on a case by case basis. A different type of phase transition, where inverse specific heat diverges, is also studied within this framework. We show that in the latter case, metric (of equilibrium state space geometry) is singular instead of curvature scalar. Since a metric singularity may be a coordinate artifact, we propose that GTD indicates that it is the singularity of specific heat and not inverse specific heat which indicates a phase transition of black holes.