  We present a geometrical derivation of the relativistic dynamics of the
superfluid inner crust of a neutron star. The resulting model is analogous to
the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component
superfluid at finite temperature, but particular attention should be paid to
the fact that some fraction of the neutrons are locked to the motion of the
protons in nuclei. This gives rise to an ambiguity in the definition of the two
currents (the normal and the superfluid one) on which the model is built, a
problem that manifests itself as a chemical gauge freedom of the theory. To
ensure chemical gauge covariance of the hydrodynamic model, the
phenomenological equation of motion for a quantized vortex should contain an
extra transverse force, that is the relativistic version of the Iordanskii
force discussed in the context of superfluid Helium. Hence, we extend the
mutual friction model of Langlois et al. (1998) to account for the possible
presence of this Iordanskii-like force. Furthermore, we propose that a better
understanding of the (still not completely settled) controversy around the
presence of the Iordanskii force in superfluid Helium, as well as in neutron
stars, may be achieved by considering that the different incompatible results
present in the literature pertain to two, opposite, dynamical regimes of the
fluid system.
