Effect of Peculiar Motion in Weak Lensing

We study the effect of peculiar motion in weak gravitational lensing. We derive a fully relativistic formula for the cosmic shear and the convergence in a perturbed Friedmann Universe. We find a new contribution related to galaxies peculiar velocity. This contribution does not affect cosmic shear in a measurable way, since it is of second order in the velocity. However, its effect on the convergence (and consequently on the magnification, which is a measurable quantity) is important, especially for redshifts z < 1. As a consequence, peculiar motion modifies also the relation between the shear and the convergence.