%0 Journal Article
%T Sharp parameter bounds for certain maximal point lenses
%A Robert Luce
%A Olivier S¨¨te
%A J£¿rg Liesen
%J Physics
%D 2013
%I arXiv
%R 10.1007/s10714-014-1736-9
%X 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.
%U http://arxiv.org/abs/1312.4778v4