Beyond the Thin Lens Approximation
arXiv:astro-ph/9504060 · doi:10.1086/176791
Abstract
We obtain analytic formulae for the null geodesics of Friedmann-Lema\^ıtre-Robertson-Walker spacetimes with scalar perturbations in the longitudinal gauge. From these we provide a rigorous derivation of the cosmological lens equation, and obtain an expression for the magnification of a bundle of light rays without restriction to static or thin lens scenarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.
37 pages plus 3 appended figures, plain TeX. Submitted to ApJ
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