Five Point Mass Gravitational Lenses in a Rhombus as a Soluble Model Giving the Maximum Number of Images

TL;DR

This paper introduces a solvable gravitational lens model with five point masses arranged in a diamond shape, providing explicit image position formulas and maximum image counts for sources behind the lens.

Contribution

It extends previous four-lens models to five lenses in a diamond configuration, enabling explicit solutions for image positions and maximum image counts.

Findings

Maximum of twenty images for five lenses.

Explicit formulas for image positions near the center.

Linear approximation for sources close to the center.

Abstract

As an extension of four point mass lenses at the vertices of a rhombus, we present five point mass lenses at the center and vertices of a diamond, which constitute, for a source behind the center, a soluble model giving expressions of all the image positions (with the maximum number of images as twenty for five lenses). For a source near the center, all the image positions are obtained in the linear approximation.