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.

This version contains heavily updated and expanded content compared to the previous version. This is a preliminary version. Comments are welcome. 30 pages