Comparison of Geodesics and Energy Variation Principles of Light Propagation

Wladimir Belayev^1,

¹Center for Relativity and Astrophysics, Saint-Petersburg, Russia

Cite this paper:
Wladimir Belayev. Comparison of Geodesics and Energy Variation Principles of Light Propagation. International Journal of Physics. 2013; 1(1):1-4. doi: 10.12691/ijp-1-1-1

Abstract

The propagation of light on a set of null paths in a pseudo-Riemannian manifold is studied using a variational principle of extremal energy. This method is compared with those based on the geodesics and Fermat principles. For the static space-time all three variational methods give the same solutions. The Fermat principle for stationary gravitational fields is identical to the principle of variation of energy of light-like particles. The approach proposed here is applied to a flat expanding space, corresponding to the LCDM-model, and generalized Gödel space-time. In the first case a solution obtained by the method of energy variation coincides with the geodesic method, while in the second case they give different solutions.

Keywords:
variational methods Lagrangian light-like particle Fermat principle geodesics

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Belayev, W.B., “Application of Lagrange mechanics for analysis of the light-like particle motion in pseudo-Riemann space”, Int. J. Th. and Math. Phys. 2(2): 10-15. Apr. 2012.
[2]	Dautcourt G., “The lightcone of Gödel-like spacetimes”, Class.Quant.Grav. 27(22). 225024. Nov. 2010, arXiv:1009.5231.
[3]	Landau L.D. and Lifshitz E.M., Classical Theory of Fields, Fourth Revised English Edition, Butterworth–Heinemann, Oxford, 273, 1975.
[4]	Pauli W, Theory of relativity, Pergamon press, New York, 1958.
[5]	McVittie G.C, General Relativity and Cosmology, London, Chapman and Hall Ltd., 1956.