Magnetically charged black holes and their stability.

We study magnetically charged black holes in the Einstein-Yang-Mills-Higgs theory in the limit of infinitely strong coupling of the Higgs field. Using mixed analytical and numerical methods we give a complete description of static spherically symmetric black hole solutins, both abelian and nonabelian. In particular we find a new class of extremal nonabelian solutions. We show that all nonabelian solutions are stable against linear radial perturbations. The implications of our results for the semiclassical evolution of magnetically charged black holes are discussed. *) On leave of absence from Institute of Physics, Jagellonian University, Cracow, Poland.