Shock waves in superconducting cosmic strings: growth of current

TL;DR

This paper investigates shock wave solutions in superconducting cosmic strings, showing how current discontinuities propagate and highlighting the stability conditions and limitations of current transitions.

Contribution

It introduces the intrinsic equations of motion for superconducting cosmic strings with shock-wave solutions and analyzes their stability and current transition constraints.

Findings

Shock waves involve current discontinuities propagating at finite velocity.

Stable shocks increase the current magnitude across the discontinuity.

Transitions between spacelike and timelike currents are impossible in these shocks.

Abstract

Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term \chi. The hypersurface of discontinuity propagates at finite velocity determined by finite increment \Delta \chi =\chi_+ -\chi_-. The current increases \chi_+>\chi_- in stable shocks but transition between spacelike (\chi >0) and timelike (\chi<0) currents is impossible.