Thermodynamics of phantom Reissner-Nordstrom-AdS black hole

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.

On thermodynamics of charged AdS black holes in extended phases space via M2-branes background

“…Since the GDM approach fails to explain the correspondence between phase transitions and singularities of the scalar curvature for phantom Reissner-Nordstrom AdS black holes, as reported in [39][40][41][42], it is legitimate and well justified hereafter to check the thermodynamic geometry of black holes metric by metric and to see the divergent points of the specific heat correspond exactly to the singularities derived by GTD method.…”

Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

“…Recently, a new solution of Einstein-anti-Maxwell theory with a cosmological constant, called the anti-ReissnerNordstrom-(A)de Sitter solution, has been investigated [18]. This new solution has led to the following thermodynamic expression for the mass of this black hole:…”

“…Quvedo's method incorporates Legendre invariance in a natural way, and it allows us to derive Legendre invariant metrics in the space of equilibrium states. However, this method not only contains certain ambiguities but also fails to explain the correspondence between phase transitions and singularities of the scalar curvature for the phantom Reissner-Nordstrom-AdS black hole [17][18][19].…”

Double shadow of a regular phantom black hole as photons couple to the Weyl tensor

“…Recently, Bronnikov et al [64] obtained a kind of solutions with phantom scalar hair, which has the properties of both black holes and wormholes. Some other black hole solutions describing gravity coupled to phantom scalar fields or phantom Maxwell fields have been found and the corresponding geometric structure and thermodynamic properties are also studied in [65][66][67][68][69][70][71][72][73]. The strong gravitational lensing of such a kind of black holes with phantom hair has been investigated in [74][75][76][77][78].…”