Transparent Spheres as Gravitational Lens

TL;DR

This paper explores gravitational lensing by transparent matter distributions, analyzing image properties, caustics, and critical curves using numerical methods and software, confirming known behaviors and identifying specific curve shapes.

Contribution

It provides a detailed analysis of gravitational lensing effects for various transparent matter profiles using numerical methods and software, expanding understanding of image formation and caustic structures.

Findings

Images follow expected patterns like odd number of images

Caustics include diamond, ellipse, and lemniscate shapes

Critical curves are mostly elliptical, with lemniscates in specific cases

Abstract

In this contribution, we present a short account of gravitational lenses and how to calculate different properties of its images in the case of having a transparent distribution of matter such as the uniform transparent sphere, isothermal gas sphere, non-singular isothermal gas sphere and a transparent King profile. With the help of XFGLenses software, and numerical methods, different images arising from all of these profiles, and the different caustics and critical curves are shown. The images were consistent with several previous results that are expected for transparent profiles, like having an odd number of images, and reducing the number of images by two when the source passes through the caustic. The curves shown in the caustics where the diamond, the ellipse and the lemniscate-like. For the critical curves, the most common curve was the ellipse, and the lemniscate appeared in the transparent NSIS case, which is consistent with the fact that these curves are common in gravitational lenses.