Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics

TL;DR

This paper explores the thermodynamic and geometric properties of a spherically symmetric phantom black hole with electric charge and dilaton, revealing phase transitions and stability changes through geometrothermodynamics and traditional thermodynamic analysis.

Contribution

It applies the Legendre invariant formalism of geometrothermodynamics to phantom black holes, identifying new phase transitions caused by phantom energy and confirming results with standard thermodynamics.

Findings

Identification of singularities in thermodynamic curvature indicating phase transitions

Discovery of a new phase transition due to phantom energy affecting black hole stability

Validation of geometrothermodynamics approach with traditional thermodynamic analysis

Abstract

We use the Legendre invariant formalism of geometrothermodynamics to investigate the geometric properties of the equilibrium space of a spherically symmetric phantom black hole with electric charge and dilaton. We find that at certain points of the equilibrium space, the thermodynamic curvature is characterized by the presence of singularities that are interpreted as phase transitions. We also investigate the phase transition structure by using the standard approach of black hole thermodynamics based upon the analysis of the heat capacity and response functions. We show compatibility between the two approaches. In addition, a new type of phase transition is found which is due to the presence of phantom energy and corresponds to a transition between black hole states with different stability properties.