Thermodynamic phase transition of Anti-de Sitter Reissner–Nordström black holes with exotic Einstein–Maxwell gravities

To consider the inevitable cosmic magnetic effects instead of the unknown dark sector of matter/energy on the inflation phase of the expanding universe some authors have proposed several extended exotic Einstein–Maxwell gravities which are addressed in this work. Some of these exotic models include directional interaction terms between the electromagnetic vector field and the metric tensor field. We use one of them to investigate the physical effects of interaction terms on the thermodynamic behavior of the modified Reissner–Nordstrom (RN) black hole. We use the perturbation series method to find analytic solutions of the field equations because of the non-linearity of the field equations which cause they do not have analytic closed form solutions. We investigate possibility of the Hawking–Page and the small/large black hole phase transition and also, effects of the interaction part of the model on possibility of the coexistence of the several phases of the perturbed AdS RN black hole under consideration.