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We investigate finite energy solutions of theEinstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1,with n>1. Our configurations are static and spherically symmetric, approachingat infinity a Minkowski spacetime background. In contrast with the Abeliancase, the contribution of the Chern-Simons term is nontrivial already in thestatic, spherically symmetric limit. Both globally regular, particle-likesolutions and black holes are constructed numerically for several values of D.These solutions carry a nonzero electric charge and have finite mass. Forglobally regular solutions, the value of the electric charge is fixed by theChern-Simons coupling constant. The black holes can be thought as non-linearsuperpositions of Reissner-Nordstrom and non-Abelian configurations. Asystematic discussion of the solutions is given for D=5, in which case theReissner-Nordstrom black hole becomes unstable and develops non-Abelian hair.We show that some of these non-Abelian configurations are stable under linear,spherically symmetric perturbations. A detailed discussion of an exact D=5solution describing extremal black holes and solitons is also provided.

Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions