Slowly Rotating Black Holes in Brans-Dicke-Maxwell Theory

In this paper, we construct a class of (n+1)-dimensional $(n\geq4)$ slowly rotating black hole solutions in Brans-Dicke-Maxwell theory with a quadratic potential. These solutions can represent black holes with inner and outer event horizons, an extreme black hole and a naked singularity and they are neither asymptotically flat nor (anti)-de Sitter. We compute the Euclidean action and use it to obtain the conserved and thermodynamics quantities such as entropy, which does not obey the area law. We also compute the angular momentum and the gyromagnetic ratio for these type of black holes where the gyromagnetic ratio is modified in Brans-Dicke theory compared to the Einstein theory.