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Pauli W, Theory of relativity, Pergamon press, New York, 1958.

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Article

Comparison of Geodesics and Energy Variation Principles of Light Propagation

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


International Journal of Physics. 2013, Vol. 1 No. 1, 1-4
DOI: 10.12691/ijp-1-1-1
Copyright © 2013 Science and Education Publishing

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.

Correspondence to: Wladimir Belayev, Center for Relativity and Astrophysics, Saint-Petersburg, Russia. Email: Corresponding author: wbelayev@yandex.ru

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.

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