NO-HAIR THEOREMS AND BLACK-HOLES WITH HAIR

The critical steps leading to the uniqueness theorem for the Kerr-Newm an metric are examined in the light of the new black hole solutions wi th Yang-Mills and scalar hair. Various methods - including scaling tec hniques, arguments based on energy conditions, conformal transformatio ns and divergence identities - are reviewed, and their range of applic ation to self-gravitating scalar and non-Abelian gauge Gelds is discus sed. In particular, the no-hair theorem is extended to harmonic mappin gs with arbitrary Riemannian target manifolds.