  It has been found that the states of the 2-charge extremal D1-D5 system are
given by smooth geometries that have no singularity and no horizon
individually, but a `horizon' does arise after `coarse-graining'. To see how
this concept extends to the 3-charge extremal system, we construct a
perturbation on the D1-D5 geometry that carries one unit of momentum charge
$P$. The perturbation is found to be regular everywhere and normalizable, so we
conclude that at least this state of the 3-charge system behaves like the
2-charge states. The solution is constructed by matching (to several orders)
solutions in the inner and outer regions of the geometry. We conjecture the
general form of `hair' expected for the 3-charge system, and the nature of the
interior of black holes in general.
