Three-dimensional scalar-tensor black holes with conformally invariant electrodynamics

We explore three-dimensional scalar-tensor black hole solutions in the presence of power-Maxwell electrodynamics. By applying the conformal transformations on the action of scalar-tensor theory, we show that the electromagnetic Lagrangian remains invariant for a specific amount of power. In addition, the gravitational action transforms to that of Einstein-dilaton gravity theory. Through solving the field equations of this theory, we obtain two novel classes of Einstein-dilaton black hole solutions. Next, proceed to investigate the thermodynamic properties of the solutions and show that thermodynamical first law is valid for both of our solutions. Then, we analyze the thermal stability or phase transition of the black holes based on the canonical ensemble method. Finally, we obtain the Jordan frame scalar-tensor black hole solutions, by imposing the inverse conformal transformations, from their Einstein-dilaton counterparts and investigate their thermodynamics and thermal stability properties.