#### Date

5-13-2015

#### Document Type

Thesis

#### Abstract

The purpose of this research was to calculate the shear and divergence of light rays bundles as they pass black holes. We defined a Lagrangian using the Schwarzchild metric then used the Euler-Lagrangian equation to create 6 first order OED’s for the light rays path. Next we found tangent vectors to the light ray so we could calculate Ψ0. In order to calculate the shear and divergence the method of calculation required simultaneously solving 16 ordinary differential equations. We used Mathematica to calculate how these light rays act but first we had to use calculus and algebra to derive these equations. We started from the Schwarzchild metric to find the Langrangian for the motion of the light rays. We then got results which were 6 ODE’s that gave velocity and acceleration in (Τ, r, θ, ϕ). Then we found the tangent vectors to these paths which allows us to solve for Ψ0 and finally we solved for the divergence and shear of the light rays.

#### Department

Physics

#### Thesis Comittee

Thomas Kling (Thesis Director)

Edward Deveney

Jeffery Williams

#### Copyright and Permissions

Original document was submitted as an Honors Program requirement. Copyright is held by the author.

#### Recommended Citation

Witherell, Matthew. (2015). Calculating the Shear and Divergence of Light Rays. In *BSU Honors Program Theses and Projects.* Item 115. Available at: https://vc.bridgew.edu/honors_proj/115

Copyright © 2015 Matthew Witherell