Regular nonminimal magnetic black holes in spacetimes with a cosmological constant

We consider new regular exact spherically symmetric solutions of a nonminimal Einstein--Yang-Mills theory with a cosmological constant and a gauge field of magnetic Wu-Yang type. The most interesting solutions found are black holes with metric and curvature invariants that are regular everywhere, i.e., regular black holes. We set up a classification of the solutions according to the number and type of horizons. The structure of these regular black holes is characterized by four specific features: a small cavity in the neighborhood of the center, a repulsion barrier off the small cavity, a distant equilibrium point, in which the metric function has a minimum, and a region of Newtonian attraction. Depending on the sign and value of the cosmological constant the solutions are asymptotically de Sitter (dS), asymptotically flat, or asymptotically anti-de Sitter (AdS).