  We present a family of exact black-hole solutions on a static spherically
symmetric background in second-order generalized Proca theories with derivative
vector-field interactions coupled to gravity. We also derive non-exact
solutions in power-law coupling models including vector Galileons and
numerically show the existence of regular black holes with a primary hair
associated with the longitudinal propagation. The intrinsic vector-field
derivative interactions generally give rise to a secondary hair induced by
non-trivial field profiles. The deviation from General Relativity is most
significant around the horizon and hence there is a golden opportunity for
probing the Proca hair by the measurements of gravitational waves (GWs) in the
regime of strong gravity.
