Geometric description of the thermodynamics of a black hole with power Maxwell invariant source

TL;DR

This paper explores the geometric structure of a nonlinear charged black hole's thermodynamics, revealing that curvature singularities in the equilibrium manifold correspond precisely to phase transition points.

Contribution

It applies geometrothermodynamics to a nonlinear charged black hole, linking geometric curvature with thermodynamic phase transitions and critical phenomena.

Findings

Curvature singularities align with phase transition points.

The equilibrium manifold is curved, indicating thermodynamic interactions.

Geometric approach effectively describes black hole thermodynamics.

Abstract

Considering a nonlinear charged black hole as a thermodynamics system, we study the geometric description of its phase transitions. Using the formalism of geometrothermodynamics we show that the geometry of the space of thermodynamic equilibrium states of this kind of black holes is related with information about thermodynamic interaction, critical points and phase transitions structure. Our results indicate that the equilibrium manifold of this black hole is curved and that curvature singularities appear exactly at those places where first and second order phase transitions occur.