Shock waves in superconducting cosmic strings: instability to extrinsic perturbations

TL;DR

This paper investigates shock wave stability in superconducting cosmic strings, revealing that shocks in the magnetic regime are stable, while those in the electric regime are susceptible to instability from extrinsic perturbations.

Contribution

It provides the first detailed stability analysis of shock-like discontinuities in superconducting cosmic strings, distinguishing conditions for stability in different current regimes.

Findings

Magnetic regime shocks are stable against extrinsic perturbations.

Electric regime shocks are unstable and do not survive perturbations.

Conditions for the existence of stable shocks are explicitly characterized.

Abstract

Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that the necessary and enough conditions for existence of stable shocks and show that the shock can be unstable in the presence of infinitesimal extrinsic perturbations of the string worldsheet. The shocks in the "magnetic" regime are not vulnerable to this instability but the shocks in the "electric" regime do not survive.