Thermodynamics of black plane solution

Abstract

We obtain a new phantom black plane solution in 4D of the Einstein-Maxwell theory coupled with a cosmological constant. We analyse their basic properties, as well as its causal structure, and obtain the extensive and intensive thermodynamic variables, as well as the specific heat and the first law. Through the specific heat and the so-called geometric methods, we analyse in detail their thermodynamic properties, the extreme and phase transition limits, as well as the local and global stabilities of the system. The normal case is shown with an extreme limit and the phantom one with a phase transition only for null mass, which is physically inaccessible. The systems present local and global stabilities for certain values of the entropy density with respect to the electric charge, for the canonical and grand canonical ensembles.