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The Fermat principle in general relativity and applications. (English) Zbl 1052.58017
Summary: 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. The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context. Moreover, Morse relations can be used to check if existing models are corrected.

MSC:
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
83C10 Equations of motion in general relativity and gravitational theory
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