Eur. Phys. J. C (2016) 76: 110
https://doi.org/10.1140/epjc/s10052-016-3949-4

Regular Article - Theoretical Physics

Geometrothermodynamics of phantom AdS black holes

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, 04510, Mexico DF, Mexico
² Dipartimento di Fisica and ICRANet, Università di Roma “La Sapienza”, 00185, Rome, Italy
³ Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad Militar Nueva Granada, Cra 11 No. 101-80, Bogotá D.E., Colombia
⁴ Departamento de Posgrado, CIIDET, AP752, 76000, Querétaro QRO, Mexico

^* e-mail: quevedo@nucleares.unam.mx

Received: 25 January 2016
Accepted: 11 February 2016
Published online: 1 March 2016

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.