NO-COSMIC-SPRING CONJECTURE

Contrary to what has been previously claimed, it is found that in the Witten bosonic superconducting cosmic-string model, the tension, defined here as a local quantity, is always positive for spacelike currents even when the effect of electric charge coupling is taken into account, this effect being only responsible for the existence of a stabilizing magnetic pressure. It is conjectured that the corresponding ''spring'' states do not exist at all, at least for this model, but also presumably for any physically reasonable theory in which current-carrying cosmic strings can form.