Thermodynamics of charged rotating solutions in Brans–Dicke gravity with Born–Infeld field

We derive new exact charged rotating solutions of (n+ 1) -dimensional brans–dicke theory in the presence of born–infeld field and investigated their properties. because of the coupling between scalar field and curvature,the field equations cannot to be solved directly. using a new conformal transformation,which transforms the einstein-dilaton–born–infeld gravity lagrangian to the brans–dicke–born–infeld gravity one,the field equations are solved. we also compute temperature,charge,mass,electric potential,and entropy; entropy,however,does not obey the area law. these quantities are invariant under conformal transformation and satisfy the first law of thermodynamics. © 2017,the author(s).