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A Morse theory for light rays on stably causal Lorentzian manifolds. (English) Zbl 0920.58019
Morse theory for lightlike geodesics joining a point with a timelike curve is presented and developed for stably causal spacetimes with boundary. Applications to gravitational lenses effect theory are given. Here some conditions on the geometry and topology of spacetime for the case of infinity or odd number of images are obtained.

MSC:
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53Z05 Applications of differential geometry to physics
83C99 General relativity
53C22 Geodesics in global differential geometry
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