Higher-dimensional solitons and black holes with a nonminimally coupled scalar field

We study higher-dimensional soliton and hairy black hole solutions of the Einstein equations nonminimally coupled to a scalar field. The scalar field has no self-interaction potential but a cosmological constant is included. Nontrivial solutions exist only when the cosmological constant is negative and the constant governing the coupling of the scalar field to the Ricci scalar curvature is positive. At least some of these solutions are stable when this coupling constant is not too large.