Effect of scalar hair on magnetically charge Euler-Heisenberg AdS black hole via extended phase transition

Abstract

In this article, we have studied numerous thermodynamical aspects and the extended phase space of the AdS magnetically charged Euler-Heisenberg BH minimally coupled to a scalar field. We investigated the ADM mass, Hawking temperature, entropy, specific heat, Gibss free energy (both locally and globally) and P-V criticality at the horizon radius. Our result shows that the maximum value for the Hawking temperature of the magnetically charged Euler-Heisenberg BHis reached at the point where the specific heat and free energy diverge, which is also the point at which the second-order phase transition takes place. We found that the magnetically charged Euler-Heisenberg BHis thermodynamically stable, with a positive heat capacity and negative Gibbs free energy. We also examined the extended second-order phase space of the considered BHin both ensembles.