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A Fermat principle for stationary space-times and applications to light rays. (English) Zbl 0819.53037
The work presents an extension of Fermat principle in optics to Lorentzian product manifolds with conformally stationary metrics. The existence and multiplicity of null geodesic lines joining a given point to a timelike curve is studied. The Morse theory is used to relate the set of these geodesic lines to the topology of the space-time. As an example, the results are applied to Kerr space-time outside the stationary limit surface.

MSC:
53Z05 Applications of differential geometry to physics
78A25 Electromagnetic theory, general
83C50 Electromagnetic fields in general relativity and gravitational theory
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