  It is well known that a superfluid rotates by forming an array of quantized
vortices. A relativistic formulation for superfluid vortex dynamics is required
for a range of problems in astrophysics and cosmology, from neutron star
interiors and radio pulsar glitches to possible dark matter condensates on
galactic scales. This paper develops a formalism for such systems, extending
the well-established variational approach to relativistic fluids to account for
the presence of a collection of quantized vortices. The model is firmly
anchored in the geometry of the problem (drawing on aspects from basic string
dynamics) and accounts for elastic aspects associated with a vortex array,
providing a precise foundation for applications which have so far been based on
somewhat ad hoc phenomenology.
