Date

12-17-2024

Document Type

Thesis

Abstract

Gravitational lensing is typically modelled using thin-lens approximations which assume that the effect of the gravitational field of the intervening mass can be adequately described by the physics of an optical lens. In this project we derived equations to model how spacetime curvature alters geodesics available to light rays directly from the principles of general relativity and used these results to produce visualizations of these effects. We began with the Robertson-Walker metric to define a flat, unperturbed space time and determined a suitable mass density model for the galaxy cluster that will act as our gravitational lens. Employing this metric and potential, we obtained from the Lagrangian an integral for the angle swept out by the light ray as it bends around the lens, which also allowed us to determine the coordinates of the light ray at a given time. Using Mathematica, we applied numerical integration techniques using this model to generate visualizations of light ray geodesics and the distortion of the source object apparent to an observer due to the gravitational lens. Additionally, we used the set of differential equations resulting from the Lagrangian to generate plots of wavefronts emanating from a particular region. This work demonstrates how the observable effects of a gravitational lens can be generated from a model built from the principles of general relativity, rather than utilizing thin-lens approximations.

Department

Physics

Thesis Committee

Dr. Thomas P. Kling, Thesis Advisor
Dr. Edward F. Deveney, Committee Member
Dr. Jennifer G. Winters, Committee Member

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