Growing hair on black holes

A black hole can carry quantum numbers that are not associated with massless gauge fields, contrary to the spirit of the ``no-hair'' theorems. In the Higgs phase of a gauge theory, electric charge on a black hole generates a nonzero electric field outside the event horizon. This field is nonperturbative in and is exponentially screened far from the hole. It arises from the cloud of virtual cosmic strings that surround the black hole. In the confinement phase, a magnetic charge on a black hole generates a classical field that is screened at long range by nonperturbative effects. Despite the sharp difference in their formal descriptions, the electric and magnetic cases are closely similar physically.