Relativistic superfluid profiles near critical surfaces

Landau's two-fluid model of superfluidity ceases to apply in regions where the condensate amplitude exhibits rapid spatial variation, such as vortex cores or in the vicinity of container walls. A recently proposed relativistic Gross-Pitaevskii-type framework treats the condensate as an independent scalar degree of freedom, enabling a controlled analysis of such regimes. We use it to construct stationary superflows close to the superfluid-normal phase boundary, and examine their stability. We obtain an exact expression for Landau's critical velocity and show that the standard Newtonian profiles (such as the near-vortex condensate depletion or the boundary-layer decay) persist unmodified in the relativistic setting. We further analyse a genuinely relativistic configuration in which an accelerated superfluid develops a phase boundary induced by Tolman temperature gradients.