Runaway Collapse of Witten Vortex Loops

We consider general properties of charged circular cosmic strings in a general family of world-sheet string models. We then specialize to a model recently proposed by Carter and Peter. This model was shown to give a good description of the features of the superconducting cosmic strings originally discovered by Witten. We derive an explicit expression for the potential determining the dynamics of the string and we present explicit expressions for the string tension and energy density as a function of string-loop radius. We also obtain explicit expressions for the wiggle and woggle speeds (speeds of transverse and longitudinal perturbations, respectively). We show that the contraction of the uniformly charged string is essentially governed by the string tension (for large loop radius) and by a {\it finite} Coulomb barrier (for small loop radius). We argue for the unobstructed contraction of a uniformly charged loop over the Coulombic barrier and its eventual collapse to a charged point. The implication of such an effect to the possible formation of naked singularities, in violation of the cosmic censorship hypothesis, is finally discussed.