Thermodynamic properties of dilaton black holes with nonlinear electrodynamics

Thermodynamics and thermal stability of novel charged dilaton black holes have been analyzed in the presence of the exponential nonlinear electrodynamics. It has been found that the scalar field can be written as the linear combination of two Liouville-type potentials. Three new classes of nonlinearly charged dilatonic black holes have been obtained as the exact solutions to the coupled scalar, electromagnetic, and gravitational field equations. The impacts of nonlinear electrodynamics on the conserved and thermodynamic quantities of the new black hole solutions have been calculated. It has been illustrated that the first law of black hole thermodynamics is valid for either of the new black hole solutions. A thermal stability or phase transition analysis has been performed making use of the canonical ensemble method. The points of type-1 and type-2 phase transitions as well as the ranges at which the new nonlinearly charged dilatonic black holes are locally stable have been determined.