Relativistic hydrodynamics of a superfluid liquid

A relativistic extension of the phenomenology describing a superfluid liquid is considered. Thermodynamic identities for the pressure and energy density are found. A variational principle is developed from which the nondissipative two-velocity equations of relativistic hydrodynamics can be derived. The equations are also expressed in hamiltonian form. An expression for the energy-momentum tensor is found. Dissipative terms in the hydrodynamics equations are considered. The limits of low velocities and zero temperature are considered in greater detail. In the zero temperature limit equations are found for a rotating superfluid liquid, and the proper vibrations of the vortex lattice are considered. It is shown how the equations can be generalized in the presence of a gravitational field. Application of the formalism to neutron stars is discussed