Rotating black branes in Brans–Dicke theory with a nonlinear electromagnetic field

This paper is devoted to obtaining a class of rotating black brane solutions of Brans–Dicke theory in the presence of a power Maxwell-invariant source. Since the field equations include the second derivatives of the scalar field, we cannot solve them, directly. Therefore, we first obtain the solutions of Einstein-dilaton gravity in the presence of a nonlinear Maxwell field, and then, by using a suitable conformal transformation, we obtain the solutions of Brans–Dicke theory with a power Maxwell-invariant source. In the next step, we discuss the geometric as well as the thermodynamic properties of the solutions. We also use the counterterm method to calculate finite action and conserved quantities. Finally, we examine the first law of thermodynamics