A Fermat principle for stationary space-times and applications to light rays

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Abstract

We present an extension of the classical Fermat principle in optics to stationary space-times. This principle is applied to study the light rays joining an event with a timelike curve. Existence and multiplicity results of light rays are proved. Moreover, Morse Relations relating the set of rays to the topology of the space-time are obtained, by using the number of conjugate points of the ray. The results hold also for stationary space-times with boundary, in particular the Kerr space-time outside the stationary limit surface.

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    Work supported by the Ministry of University and Scientific and Technological Research (40%–60%, 1991).

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