Cosmic Strings Lens Phenomenology: General Properties of Distortion   Fields
  We reconsider the general properties of gravitational lensing effects induced by cosmic string systems, taking into account their equation of state and motion equations. We explicitly show that the deflection patterns induced by a string is equivalent to the one of a lineic and static distribution of matter. We then rigorously show that the convergence part of the deformation field is always zero, except on the intersection of the string worldsheet and the observer past light cone, extending previous results obtained in peculiar cases. Phenomenological consequences of this result on multiple image systems are investigated. 
Jean-Philippe Uzan and Francis Bernardeau