Bardeen-Kiselev black hole with cosmological constant

Abstract

In this work we analyze a solution that mimics the Bardeen solution with a cosmological constant surrounded by quintessence. We show that this solution can be obtained by Einstein equations coupled with nonlinear electrodynamics. We also show that the solution is not always regular and what the conditions for regularity are. We analyze the thermodynamics associated with this type of solution by establishing the form of the Smarr formula and the first law of thermodynamics. We obtain some thermodynamic quantities such as pressure, temperature, heat capacity and isothermal compressibility. Once we have these thermodynamic quantities, we check if this solution has phase transitions and how it behaves at the points where the transitions occur. For some values of the parameters, we find that the solution exhibits a first-order phase transition, like a van der Waals fluid.