  We describe a new type of hair on supersymmetric black string and black ring
solutions, which produces the largest known violation of black hole uniqueness,
parameterized by an arbitrary function and hence an infinite number of
continuous parameters. The new solutions can have non-trivial density profiles
for the electric fields along the horizon, and yet have a geometry that is
regular, although generically not infinitely differentiable, at the horizon.
Both neutral and charged probes can cross the horizon without experiencing
divergent forces. We also find restricted examples, parameterized by a few
arbitrary continuous parameters, where the charge densities fluctuate but the
metric does not and hence is completely differentiable. Our new class of
solutions owes its existence to a mechanism reminiscent of the Q-ball: in the
simplest examples the metric has more symmetry than the matter that supports
it.
