Snellius meets Schwarzschild - Refraction of brachistochrones and time-like geodesics
Popular Physics
2018-09-05 v1
Abstract
The brachistochrone problem can be solved either by variational calculus or by a skillful application of the Snellius' law of refraction. This suggests the question whether also other variational problems can be solved by an analogue of the refraction law. In this paper we investigate the physically interesting case of free fall in General Relativity that can be formulated as a variational problem w. r. t. proper time. We state and discuss the corresponding refraction law for a special class of spacetime metrics including the Schwarzschild metric.
Keywords
Cite
@article{arxiv.1809.00355,
title = {Snellius meets Schwarzschild - Refraction of brachistochrones and time-like geodesics},
author = {Heinz-Jürgen Schmidt},
journal= {arXiv preprint arXiv:1809.00355},
year = {2018}
}