Dilaton black holes with power law electrodynamics

Here we obtain the new four-dimensional black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory. We solve the coupled scalar, electromagnetic, and gravitational field equations in a static and spherically symmetric geometry and show that dilatonic potential, as the solution to the scalar field equation, can be written as a generalized Liouville potential. We obtain three classes of novel charged dilaton black hole solutions, in the presence of power law nonlinear electrodynamics, which are asymptotically nonflat and non-anti-de Sitter. Then we calculate the conserved and thermodynamic quantities from geometrical and thermodynamical approaches, separately. Since the results of these two alternative approaches are identical, one can argue that the first law of black hole thermodynamics is valid for all of the new black hole solutions. We study thermodynamic stability or phase transition of the black holes using the canonical ensemble method. The points of type-1 and type-2 phase transitions and the ranges at which the black holes remain stable are indicated by considering the heat capacity of the black hole solutions. The global stability of the black holes is studied through the grand canonical ensemble method. Regarding the Gibbs free energy of the black holes, we find the points of Hawking-Page phase transition and ranges of the horizon radii at which the black holes are globally stable.