Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2
Abstract
We have studied optical metrics via null geodesics and optical-mechanical formulation of classical mechanics, and described the geometry and optics of mechanical systems with drag dependent quadratically on velocity. Then we studied null geodesics as a central force system, deduced the related Binet's equation applied the analysis to other solutions of Einstein's equations in spherically symmetric spaces, paying special attention to the Tomimatsu-Sato metric. Finally, we examined the dualities between different systems arising from conformal transformations that preserve the Jacobi metric.
Keywords
Cite
@article{arxiv.1704.01830,
title = {Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2},
author = {Sumanto Chanda and Partha Guha},
journal= {arXiv preprint arXiv:1704.01830},
year = {2018}
}
Comments
This version contains heavily updated and expanded content compared to the previous version. This is a preliminary version. Comments are welcome. 30 pages