Abstract

In classical electrodynamics, boundary conditions of the E and B fields are derived from Maxwell's equations, which are used to derive the Fresnel equations describing the behavior of a wave at an interface between media with given indices of refraction. Though electrodynamics and gravity are in some instances strikingly analogous, boundary conditions in general relativity are somewhat more opaque. We will see that while while continuity of the metric must be true in general, discontinuity of the extrinsic curvature of spacetime, while allowed by the Einstein field equations, results in a singularity in the energy-momentum tensor. This singularity is interpreted as a surface mass density. Unlike in electrodynamics, there is an additional refractive effect of the spacetime metric. Its origin considered, a gravitational refractive index will be treated similarly to the electromagnetic refractive index. Attempts to derive gravitational "Fresnel equations" follow.

First Advisor

David C. Latimer

Degree Type

Dissertation/Thesis

Rights

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License

Degree Name

Bachelor of Science in Physics

Date of Award

Spring 5-14-2017

Department

Physics