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.

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

GIANNONI, Fabio;
1995

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/241526
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