  We study the propagation of a massive vector or Proca field on the
Schwarzschild spacetime. The field equations are reduced to a one-dimensional
wave equation for the odd-parity part of the field and two coupled equations
for the even-parity part of the field. We use numerical techniques based on
solving (scalar or matrix-valued) three-term recurrence relations to compute
the spectra of both quasi-normal modes and quasi-bound states, which have no
massless analogue, complemented in the latter case by a forward-integration
method. We study the radial equations analytically in both the near-horizon and
far-field regions and use a matching procedure to compute the associated
spectra in the small-mass limit. Finally, we comment on extending our results
to the Kerr geometry and its phenomenological relevance for hidden photons
arising e.g. in string theory compactifications.
