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The Fermat Principle in General Relativity and Applications

Fabio Giannoni·Antonio Masiello·Paolo Piccione
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Abstract

In this paper we use a general version of Fermat's principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. As a physical meaning, one can apply the Morse relations to have a mathematical description of the "gravitational lens effect" in a very general context.

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Fabio Giannoni, Antonio Masiello, Paolo Piccione. 1999-06-25. The Fermat Principle in General Relativity and Applications. https://arxiv.org/abs/math-ph/9906023

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