Torsion effects on vortex filaments and Hasimoto soliton transformation in magnetars

Abstract

The role played by torsion of magnetic vortex line curves or filaments, in the equilibrium state of magnetars is investigated. When the magnetars equilibrium equations are written in terms Frenet-Serret frame it is shown that in regions of the magnetic star where the Frenet torsion is constant it induces an oscillation in the vortex filaments. By solving the magnetar equilibrium equation we shown the this behaviour also appears in the magnetic field. The first derivative of the gravitational potential with respect to the arc lenght of the vortex filament is shown to coincide with the Hasimoto soliton transformation of the Schroedinger equation for the constant torsion.