  We study the transformation under the String Theory duality group of the
observable charges (mass, angular momentum, NUT charge, electric, magnetic and
different scalar charges) of four dimensional point-like objects whose
asymptotic behavior constitutes a subclass closed under duality. The charges
fall into two complex four-dimensional representations of the duality group. T
duality (including Buscher's) has an O(1,2) action on them and S duality a U(1)
action. The generalized Bogomol'nyi bound is an U(2,2)-invariant built out of
one representations while the other representation (which includes the angular
momentum) never appears in it. The bound is manifestly duality-invariant.
Consistency between T duality and supersymmetry requires that primary scalar
hair is included in the Bogomol'nyi bound. Four-dimensional supersymmetric
massless black holes are the T duals in time of massive supersymmetric black
holes. Non-extreme massless ``black holes'' are the T duals of the non-extreme
black holes and have primary scalar hair and naked singularities.
