In this project, I have tried to review the history and current state of Gravitational Lensing and a special case of it called the Einstein Cross, and I have tried to make it accessible to a student who may not be familiar with the Theory of General Relativity.

Gravitational Lensing is a very useful tool in astrophysics, cosmology, and also in theoretical physics. It has revealed certain features of the universe which would otherwise be too dim to see, for example, the detection of water in a very early universe quasar. It has helped in constraining many cosmological parameters and in calculating the mass of many galaxies and galaxy clusters.

In the Methods, I discussed the theoretical derivation for strong lensing using the variational principle and perturbation theory, with some discussion about strong and weak lensing. I then discussed how the unlensed source and lensed source images are related by a transformation matrix, which governs the magnification factor of the lensed image.

I then discussed what are the essential conditions a good GL candidate should satisfy for both point light sources like quasars and extended sources like galaxies. I discussed the 3 basic ways to model a gravitational lens.

In the Results, I discussed the first detection of a gravitationally lensed system apart from the sun, and the 1st detection of a quadruply lensed quasar. I drew comparisons between the observed images and the modeled images for the Einstein Cross and I discussed the limitations of using the basic lens models in for the first detection of GL.

We see that for strong lensing, the calculated deflection angle is approximately useful in most scenarios, and that there are several challenges in distinguishing between two different images and two images of the same object. Weak lensing, on the other hand, is not as well described by these equations, as we need a different metric itself, to solve for this case.

With the release of the James Webb Space Telescope, we are able to probe much farther away than Hubble could, and we are slowly getting to the time when it was just a few million years after the big bang. The use of artificial intelligence and neural networks are also promising improvements in the analysis of GL systems, and this will further increase the frequency with which we observe GLs and understand several aspects of the universe.

THANK YOU!