Geometrothermodynamics of phantom AdS black holes

Abstract

We show that to investigate the thermodynamic properties of charged phantom spherically symmetric anti-de-Sitter black holes, it is necessary to consider the cosmological constant as a thermodynamic variable so that the corresponding fundamental equation is a homogeneous function defined on an extended equilibrium space. We explore all the thermodynamic properties of this class of black holes by using the classical physical approach, based upon the analysis of the fundamental equation, and the alternative mathematical approach as proposed in geometrothermodynamics. We show that both approaches are compatible and lead to equivalent results.

12 latex pages, no figures

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• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Unified geometric description of black hole thermodynamics
• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
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• Phase transition and heat engine efficiency of phantom AdS black holes
• Phantom RN-AdS black holes in noncommutative space
• A consistent and unified picture for critical phenomena of $f(R)$ AdS black holes
• Area products for ${\mathcal{H}}^{\pm }$ in AdS space