Covariant vortex in superconducting-superfluid-normal fluid mixtures with a stiff equation of state

Abstract

Using a covariant description, we obtain the integrals of motion for a cylindrically symmetric, stationary vortex configuration in a mixture of interacting superconductors, superfluids and normal fluids. We then integrate the stress-energy density and find a very simple, closed expression for the energy per unit length and the relevant stress coefficients of the vortex with respect to a vortex-free reference state. This result is found assuming a ``stiff'' equation of state for the fluid mixture, which is the least compressible but still causal equation of state (contrary to the incompressible case). As an illustration for these general results, we discuss some applications to ``real'' superfluid-superconducting systems that are contained as special cases. These include the two-fluid model for He-II, uncharged binary superfluid mixtures, conventional superconductors and the superfluid neutron-proton-electron plasma in the outer core of neutron stars.