A Morse Theory for Massive Particles and Photons in General Relativity
Mathematical Physics
2009-10-31 v1 Differential Geometry
math.MP
Abstract
In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the paper we discuss a limit process that allows to obtain also a Morse theory for light rays.
Cite
@article{arxiv.math-ph/9905009,
title = {A Morse Theory for Massive Particles and Photons in General Relativity},
author = {Fabio Giannoni and Antonio Masiello and Paolo Piccione},
journal= {arXiv preprint arXiv:math-ph/9905009},
year = {2009}
}