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Alternative theories of gravity and their solutions are of considerableimportance since at some fundamental level the world can reveal new features.Indeed, it is suspected that the gravitational field might be nonminimallycoupled to the other fields at scales not yet probed, bringing into theforefront nonminimally coupled theories. In this mode, we consider a nonminimalEinstein-Yang-Mills theory with a cosmological constant. Imposing sphericalsymmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for theYang-Mills field, we find expressions for the solutions of the theory. Furtherimposing constraints on the nonminimal parameters, we find a family of exactsolutions of the theory depending on five parameters, namely, two nonminimalparameters, the cosmological constant, the magnetic charge, and the mass. Thesesolutions represent magnetic monopoles and black holes in magnetic monopoleswith de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on thesign and value of the cosmological constant $\Lambda$. We classify completelythe family of solutions with respect to the number and the type of horizons andshow that the spacetime solutions can have, at most, four horizons. Forparticular sets of the parameters, these horizons can become double, triple,and quadruple. For instance, for a positive cosmological constant $\Lambda$,there is a critical $\Lambda_c$ for which the solution admits a quadruplehorizon, evocative of the $\Lambda_c$ that appears for a given energy densityin both the Einstein static and Eddington-Lema\^{\i}tre dynamical universes. Asan example of our classification, we analyze solutions in the Drummond-Hathrellnonminimal theory that describe nonminimal black holes. Another application iswith a set of regular black holes previously treated.

Magnetic black holes and monopoles in a nonminimal Einstein-Yang-Mills theory with a cosmological constant: Exact solutions