  We show that scalar hair can be added to rotating, vacuum black holes of
general relativity. These hairy black holes (HBHs) clarify a lingering question
concerning gravitational solitons: if a black hole can be added at the centre
of a boson star, as it typically can for other solitons. We argue that it can,
but only if it is spinning. The existence of such HBHs is related to the Kerr
superradiant instability triggered by a massive scalar field. This connection
leads to the following conjecture: a (hairless) black hole which is afflicted
by the superradiant instability of a given field must allow hairy
generalizations with that field.
