Gravitating sphalerons and sphaleron black holes in asymptotically anti–de Sitter spacetime

Numerical arguments are presented for the existence of spherically symmetric regular and black hole solutions of the Einstein-Yang-Mills-Higgs equations with a negative cosmological constant. These solutions approach asymptotically the anti–de Sitter spacetime. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. The instability of the gravitating sphaleron solutions is also proven.