  General relativistic superfluid neutron stars have a significantly more
intricate dynamics than their ordinary fluid counterparts. Superfluidity allows
different superfluid (and superconducting) species of particles to have
independent fluid flows, a consequence of which is that the fluid equations of
motion contain as many fluid element velocities as superfluid species. Whenever
the particles of one superfluid interact with those of another, the momentum of
each superfluid will be a linear combination of both superfluid velocities.
This leads to the so-called entrainment effect whereby the motion of one
superfluid will induce a momentum in the other superfluid. We have constructed
a fully relativistic model for entrainment between superfluid neutrons and
superconducting protons using a relativistic $\sigma - \omega$ mean field model
for the nucleons and their interactions. In this context there are two notions
of ``relativistic'': relativistic motion of the individual nucleons with
respect to a local region of the star (i.e. a fluid element containing, say, an
Avogadro's number of particles), and the motion of fluid elements with respect
to the rest of the star. While it is the case that the fluid elements will
typically maintain average speeds at a fraction of that of light, the
supranuclear densities in the core of a neutron star can make the nucleons
themselves have quite high average speeds within each fluid element. The
formalism is applied to the problem of slowly-rotating superfluid neutron star
configurations, a distinguishing characteristic being that the neutrons can
rotate at a rate different from that of the protons.

General Relativity and Quantum Cosmology;Astrophysics