We explore (n+1)-dimensional (Formula: see text) charged black holes (BHs) in the scalar-tensor (ST) gravity theory. By varying the Jordan frame (JF) action of (n+1)-dimensional ST gravity, the equations of motion are obtained which are strongly dependent on each other and very difficult to solve. To get rid of this problem, conformal transformations (CTs) are used in the form Formula: see text by use of which, the JF action is transformed to the Einstein frame (EF). After obtaining the exact solutions of the (n+1)-dimensional Einstein-dilaton theory, it is shown that, due to existence of the scalar field, the metric function posses an unusual asymptotic behavior. The conserved and thermodynamic quantities of dilatonic BHs are calculated and validity of the first law of thermodynamics (FLT) is investigated. Thermodynamic stability or phase transition (PT) of dilatonic BHs is analyzed by using the canonical ensemble method. Finally, with the help of inverse CTs, the charged ST-Maxwell BHs are obtained from their Einstein-dilatonic counterparts and their thermodynamic properties are studied.
Karimi et al. (Thu,) studied this question.