Dynamics of a relativistic Rankine vortex for a two-constituent superfluid in a weak perturbation of cylindrical symmetry

TL;DR

This paper generalizes the classical Rankine vortex to a relativistic superfluid context, analyzing its dynamics under weak perturbations and deriving Nambu-Goto equations for the vortex core.

Contribution

It introduces a relativistic extension of the Rankine vortex for superfluids and derives the vortex dynamics using Nambu-Goto equations under weak perturbations.

Findings

Relativistic Rankine vortex solution proposed

Derived Nambu-Goto equations for vortex dynamics

Analyzed weak perturbation effects on vortex core

Abstract

From a recent study of a stationary cylindrical solution for a relativistic two-constituent superfluid at low temperature limit, we propose to specify this solution under the form of a relativistic generalisation of a Rankine vortex (Potential vortex whose the core has a solid body rotation).Then we establish the dynamics of the central line of this vortex by supposing that the deviation from the cylindrical configuration is weak in the neighbourhood of the core of the vortex. In "stiff" material the Nambu-Goto equations are obtained.