TRANSFORMATION OF BLACK-HOLE HAIR UNDER DUALITY AND SUPERSYMMETRY

We study the transformation under the full string theory duality group of the observable charges (including mass, angular momentum, NUT char ge, electric, magnetic and different scalar charges) of four-dimension al point-like objects whose asymptotic behavior constitutes subclass c losed under duality. We find that those charges fall into two complex four-dimensional representations of the duality group, T-duality (incl uding Buscher's transformations) has an O(1,2) action on them and S-du ality a U(1) action, The generalized Bogomol'nyi bound is an U(2,2)-in variant built out of one representation while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T-duality and sup ersymmetry seems to require that primary scalar hair is included in th e generalized Bogomol'nyi bound, We also find that all known four-dime nsional supersymmetric massless black holes are the T-duals in the tim e direction of the usual massive supersymmetric black holes, Non-extre me massless ''black holes'' can be found as the T-duals of the non-ext reme black holes, All of them have primary scalar hair and naked singu larities. (C) 1997 Elsevier Science B.V.