Creating images by adding masses to gravitational point lenses

Abstract

A well-studied maximal gravitational point lens construction of S. H. Rhie produces $5n$ images of a light source using $n+1$ deflector masses. The construction arises from a circular, symmetric deflector configuration on $n$ masses (producing only $3n+1$ images) by adding a tiny mass in the center of the other mass positions (and reducing all the other masses a little bit). In a recent paper we studied this "image creating effect" from a purely mathematical point of view (Sète, Luce & Liesen, Comput. Methods Funct. Theory 15(1):9-35, 2015). Here we discuss a few consequences of our findings for gravitational microlensing models. We present a complete characterization of the effect of adding small masses to these point lens models, with respect to the number of images. In particular, we give several examples of maximal lensing models that are different from Rhie's construction and that do not share its highly symmetric appearance. We give generally applicable conditions that allow the construction of maximal point lenses on $n+1$ masses from maximal lenses on $n$ masses.

Minor corrections, update some references, to appear in GRG

References in corpus (4)

• n-point Gravitational Lenses with 5(n-1) Images
• Perturbing rational harmonic functions by poles
• A Note on the Maximum Number of Zeros of $r(z)-\bar{z}$
• Sharp parameter bounds for certain maximal point lenses

Cited by in corpus (7)

• Image-plane Analysis of n-point-mass Lens Critical Curves and Caustics
• A Newton method for harmonic mappings in the plane
• The maximum number of zeros of $r(z)-\overline{z}$ revisited
• How constant shifts affect the zeros of certain rational harmonic functions
• On the Number of Equilibria Balancing Newtonian Point Masses with a Central Force
• The transport of images method: computing all zeros of harmonic mappings by continuation
• Multiplane gravitational lenses with an abundance of images