Nonlinearly charged scalar-tensor black holes in ( 2+1 ) dimensions

Abstract

The action of three-dimensional charged Einstein-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory by utilizing the suitable conformal transformations. The field equations of the Einstein-dilaton gravity coupled to the power Maxwell nonlinear electrodynamics have been solved and two new classes of static and spherically symmetric charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained. Also, the dilaton potential has been written as the linear combination of two Liouville-type potentials. The black hole conserved charges and thermodynamic quantities have been calculated by utilizing the geometrical and thermodynamical methods, separately. The compatibility of the results obtained from these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions in the Einstein frame. A black hole stability or phase transition analysis has been performed in the context of the canonical ensemble. By calculating the black hole heat capacity, with the black hole charge as a constant, the type one and type two phase transition points have been determined. Also, the ranges of the black hole horizon radii at which the Einstein black holes are thermally stable have been identified for both of the new black hole solutions. Then making use of the inverse conformal transformations, two new classes of the scalar-tensor black holes have been obtained from their Einstein frame counterparts. The thermodynamic properties and thermal stability of the new scalar-tensor black holes have been investigated. It has been found that the new charged black holes have the same thermodynamic behaviors in both of the Einstein and Jordan frames.