GAUGE-SYMMETRY BREAKDOWN AT THE HORIZON OF EXTREME BLACK-HOLES

Static solutions of the Einstein-Yang-Mills-Higgs system containing ex treme black holes are studied. The field equations imply strong restri ctions on boundary values of all fields at the horizon. If the Yang-Mi lls radial electric field E is non-zero there, then all fields at the horizon take values in the centralizer of E. For the particular case o f SU(3), there are two different kinds of centralizers: two-dimensiona l Abelian (Cartan subalgebra) and four-dimensional (su(2) x u(1)) ones . The two-dimensional centralizer admits only constant fields: even th e geometry of the horizon is that of constant curvature. If the cosmol ogical constant Lambda is negative, a 2-surface of any genus is possib le; for positive curvature, only spherically symmetrical horizons are allowed. For the four-dimensional centralizer, all spherically symmetr ical horizons are explicitly given. Finally, some complete spacetime s olutions are constructed whose horizons have the structure found by ou r method. There are also Abelian solutions of a new type. In some case s there are different spacetimes having the same type of horizon.