Gravitational lens optical scalars in terms of energy–momentum distributions in the cosmological framework

Abstract

We present new results on gravitational lensing over a cosmological Robertson-Walker backgrounds which extend and generalize previous works. Our expressions show the presence of new terms and factors which have been neglected in the literature on the subject. The new equations derived here for the optcal scalars allow to deal with more general matter content including sources with non Newtonian components of the energy-momentum tensor and arbitrary motion. Our treatment is within the framework of weak gravitational lenses in which first order effects of the curvature are considered. We have been able to make all calculations without referring to the concept of deviation angle. This in turn, makes the presentation shorter but also allows for the consideration of global effects on the Robertson-Walker background that have been neglected in the literature. We also discuss two intensity magnification, that we define in this article; one coming from a natural geometrical contruction in terms of the affine distance, that here we call $\tilde{\mu}$, and the other adapted to cosmological discussions in terms of the redshift, that we call $\mu'$. We show that the natural intensity magnification $\tilde{\mu}$ coincides with the standard solid angle magnification ($\mu$).