Beyond the Thin Lens Approximation

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Abstract
We obtain analytic formulae for the null geodesics of Friedmann-Lema^{i}tre-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.Comment: 37 pages plus 3 appended figures, plain TeX. Submitted to Ap

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