Reduction of the gravitational lens equation to a one-dimensional non-linear form for the tilted Plummer model family

TL;DR

This paper simplifies the gravitational lens equation for the tilted Plummer model family into one-dimensional non-linear and polynomial forms, facilitating the analysis of image formation and caustics in gravitational lensing.

Contribution

It introduces a reduction of the lens equation to simpler forms for the tilted Plummer models, aiding in the efficient computation of images and caustics.

Findings

Reduction to one-dimensional non-linear equations

Polynomial form for specific slope values

Up to five images can be produced by the model

Abstract

The gravitational lens equation for the tilted Plummer family of models can be reduced to a one-dimensional non-linear equation. For certain values of the slope of the radial profile it can be reduced to a polynomial form. Both forms are advantageous to find the roots, i.e. the images for a given model. The critical curve equations can also be reduced to a non-linear or polynomial form, and therefore it is useful to find the caustics. This lens model family has ample use in gravitational lens theory, and can produce up to five images.