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 static distribution of matter localized on a line. We then rigorously show that the convergence part of the deformation field is always zero, except on the intersection of the string world sheet and the observer past light cone, extending previous results obtained in peculiar cases. Phenomenological consequences of this result on multiple image systems are investigated.