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arXiv · 1312.4778

Sharp parameter bounds for certain maximal point lenses

Robert Luce·Olivier Sète·Jörg Liesen
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Abstract

Starting from an $n$-point circular gravitational lens having $3n+1$ images, Rhie (2003) used a perturbation argument to construct an $(n+1)$-point lens producing $5n$ images. In this work we give a concise proof of Rhie's result, and we extend the range of parameters in Rhie's model for which maximal lensing occurs. We also study a slightly different construction given by Bayer and Dyer (2007) arising from the $(3n+1)$-point lens. In particular, we extend their results and give sharp parameter bounds for their lens model. By a substitution of variables and parameters we show that both models are equivalent in a certain sense.

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Robert Luce, Olivier Sète, Jörg Liesen. 2013-12-17. Sharp parameter bounds for certain maximal point lenses. https://doi.org/10.1007/s10714-014-1736-9

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