# Finding Singularities in Gravitational Lensing

## TL;DR

This paper develops algorithms to detect singularities in gravitational lensing systems, enabling better modeling of complex lenses and leveraging unstable caustics for astrophysical insights.

## Contribution

It introduces a novel compact representation of lens systems using A3-lines and singular points, facilitating analysis of complex gravitational lenses.

## Key findings

- Algorithms successfully detect singularities in various lens models.
- Application to Abell 697 demonstrates practical utility.
- Representation captures detailed lens features in a single snapshot.

## Abstract

The number of strong lens systems is expected to increase significantly in ongoing and upcoming surveys. With an increase in the total number of such systems we expect to discover many configurations that correspond to unstable caustics. In such cases, the instability can be used to our advantage for constraining the lens model. We have implemented algorithms for detection of different types of singularities in gravitational lensing. We test our approach on a variety of lens models and then go on to apply it to the inferred mass distribution for Abell 697 as an example application. We propose to represent lenses using A3-lines and singular points (A4 and D4) in the image plane. We propose this as a compact representation of complex lens systems that can capture all the details in a single snapshot.