Regular and black-hole solutions of the Einstein-Yang-Mills-Higgs equations; the case of nonminimal coupling

Regular and black-hole solutions of the spontaneously broken Einstein-Yang-Mills-Higgs theory with nonminimal coupling to gravity are shown to exist. The main characteristics of the solutions are presented and differences with respect to the minimally coupled case are studied. Since negative energy densities are found to be possible, traversable wormhole solutions might exist. We prove that they are absent.