On geodesics of gradient-index optical metrics and the optical-mechanical analogy
Abstract
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is conformally related to the metric of the ambient space. Various aspects of the optical-mechanical analogy are discussed as they relate to the geodesics of conformally related metrics. Some applications of the concepts of gradient-index optics to general relativity are examined, such as effective indices of refraction for gravitational lensing and Gordon's optical metrics for optical media that are in a state of relative motion with respect to an observer. The latter topic is approached from the standpoint of pre-metric electromagnetism.
Keywords
Cite
@article{arxiv.2002.04390,
title = {On geodesics of gradient-index optical metrics and the optical-mechanical analogy},
author = {D. H. Delphenich},
journal= {arXiv preprint arXiv:2002.04390},
year = {2020}
}
Comments
31 pages. Error concerning derivation of Levi-Civita action functional corrected