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

We derive new exact charged rotating solutionsof (n+1)-dimensional Brans–Dicke theory in the presenceof 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 anew conformal transformation, which transforms the Einstein-dilaton–Born–Infeld gravity Lagrangian to the Brans–Dicke–Born–Infeld gravity one, the field equations aresolved. We also compute temperature, charge, mass, electricpotential, and entropy; entropy, however, does not obeythe area law. These quantities are invariant under conformaltransformation and satisfy the first law ofthermodynamics.