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.
David C. Latimer
Bachelor of Science in Physics
Date of Award
Litterer, Jake, "Gravitational wave behavior at a vacuum-matter interface" (2017). Honors Program Theses. 24.