General gravitational lenses of cosmological systems

OSVALDO M. MORESCHI; EZEQUIEL BOERO

Valencia

Congreso; GR22/Amaldi13; 2019

One of the main observational tools in astrophysical systems is through the study of the gravitational lenseffects caused by the object of interest. So, there are numerous works that tackle the problem of weak gravitationallenses under different assumptions; but in [1] we were able to generalize previous works by relaxing the severeassumptions of Newtonian behavior in the usual weal lens studies[2, 3]. However, there are just few works that dealwith weak gravitational lenses that work with this considerations and include the effects of the cosmic environmentinto account. We present here a detail study from first principles of the weak gravitational lens effects when thesystem is embedded in a cosmological framework. Our formulas have the advantage of being explicitly gaugeinvariant and allow us to include more general forms of matter distributions than those discussed in most standardreferences on the subject.We present new results on gravitational lensing over cosmological Robertson?Walker backgrounds which extendand generalize previous works. Our expressions show the presence of new terms and factors which have beenneglected in the literature on the subject. We make no a priori assumptions on the nature of the lens so, the newequations derived here for the optical scalars allow to deal with more general matter content including sources withnon-Newtonian components of the energy?momentum tensor and arbitrary motion. We have been able to make allcalculations without referring to the concept of deviation angle. This in turn, makes the presentation shorter butalso allows for the consideration of global effects on the Robertson?Walker background that have been overlookedin the literature.We also discuss two intensity magnifications that we define in this article; one coming from the natural physicalconstruction in terms of observed flux and the affine distance, that we here call μ̃, and the other adapted tocosmological discussions in terms of the redshift, that we call μ_0 . We show that the natural intensity magnificationμ̃ coincides with the standard angular magnification (μ).The expressions that we present are a tool to study in more detail the missing mass problem; since we introduceequations describing gravitational lenses that describe more general situations; enabling the characterization of moregeneral energy momentum tensors, in contrast to the usual Newtonian description of the dark matter phenomena.Our expressions do not neglect spacelike components of the energy momentum tensor.An interesting new result is for example the presence of a redshift factor correcting the widely used expressionsof thin lenses as appears in eq. (51), part 1 of reference [4] or eq. (16) of reference [5].