Thermodynamics of charged rotating solutions in Brans\u2013Dicke gravity with Born\u2013Infeld field

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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.