On a Fermat principle in general relativity. A Morse theory for light rays |
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| Authors: | Fabio Giannoni Antonio Masiello |
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| Affiliation: | (1) Dipartimento di Energetica, Università de L'Aquila, I-67010 L'Aquila, Italy;(2) Dipartimento di Matematica, Politecnico di Bari, Via E. Orabona 4, I-70125 Bari, Italy |
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| Abstract: | In this paper an infinite dimensional Morse theory for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds is developed under intrinsic assumptions. It yields applications to the gravitational lens effect. In particular we show that the number of images in the gravitational lens effect is infinite or odd. |
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