Thermodynamics of phantom Reissner-Nordstrom-AdS black hole

TL;DR

This paper introduces a new anti-Reissner-Nordstrom-(A)dS black hole solution within Einstein-anti-Maxwell theory, analyzing its thermodynamic properties, stability, and phase transitions using traditional and Geometrothermodynamics methods.

Contribution

It presents a novel black hole solution and compares thermodynamic analysis methods, highlighting discrepancies between traditional and Geometrothermodynamics approaches.

Findings

The anti-RN-(A)dS solution's thermodynamics are established.

Discrepancies are found between Geometrothermodynamics and traditional methods.

The stability of the solution is analyzed in different thermodynamic ensembles.

Abstract

We obtain a new solution of the Einstein-anti-Maxwell theory with cosmological constant, called anti-Reissner-Nordstrom-(A)de Sitter (anti-RN-(A)dS) solution. The basic properties of this solution is reviewed. Its thermodynamics is consistently established, with the extreme cases and phase transitions, where the analysis is performed through two methods, the usual one and that of Geometrothermodynamics . The Geometrothermodynamics analysis does not provide a result in agreement with the usual method or by the specific heat. We establish local and global thermodynamic stabilities of anti-RN-AdS solution through the specific heat and the canonical and grand-canonical ensembles.