Thermodynamics of phantom black holes in Einstein-Maxwell-Dilaton theory

TL;DR

This paper investigates the thermodynamics of phantom black holes within Einstein-Maxwell-Dilaton theory, comparing different analytical methods, and finds stability conditions and limitations of the Geometrothermodynamics approach.

Contribution

It provides a detailed thermodynamic analysis of phantom black holes, highlighting the limitations of GTD and identifying stability conditions for solutions.

Findings

GTD results mismatch with specific heat analysis, indicating limitations of the method.

Normal and phantom solutions are generally unstable unless specific parameters are met.

Anti-Reissner-Nordstrom solutions lack extremal and phase transition points.

Abstract

A thermodynamic analysis of the black hole solutions coming from the Einstein-Maxwell-Dilaton theory (EMD) in 4D is done. By consider the canonical and grand-canonical ensemble, we apply standard method as well as a recent method known as Geometrothermodynamics (GTD). We are particularly interested in the characteristics of the so called phantom black hole solutions. We will analyze the thermodynamics of these solutions, the points of phase transition and their extremal limit. Also the thermodynamic stability is analyzed. We obtain a mismatch of the between the results of the GTD method when compared with the ones obtained by the specific heat, revealing a weakness of the method, as well as possible limitations of its applicability to very pathological thermodynamic systems. We also found that normal and phantom solutions are locally and globally unstable, unless for certain values of the coupled constant of the EMD action. We also shown that the anti-Reissner-Nordstrom solution does not posses extremal limit nor phase transition points, contrary to the Reissner-Nordstrom case.