  The macroscopic dynamics of a rotating superfluid deviates from that of a
simple perfect fluid due to the effect of vorticity quantisation, which gives
rise to a substructure of cosmic string type line defects that results in a
local anisotropy whereby the effective average pressure in the direction of the
vortex lines is reduced below its value in lateral directions. Whereas previous
descriptions of this effect have been restricted to a non-relativistic
framework that is adequate for the treatment of liquid helium in a laboratory
context, the present work provides a fully relativistic description of the kind
required for application to rotating neutron star models. To start with, the
general category of vortex fibration models needed for this purpose is set up
on the basis of a Kalb-Ramond type variational principle. The appropriate
specification of the particular model to be chosen within this category will
ultimately be governed by the conclusions of microscopic investigations that
have not yet been completed, but the results available so far suggest that a
uniquely simple kind of model with an elegant dilatonic formulation should be
tentatively adopted as a provisional choice so long as there is no indication
that a more complicated alternative is needed.
