J. Ehlers

Title: Null Geodesics and Light Cones in General Relativity

Abstract: The propagation of electromagnetic radiation from distant sources (stars, galaxies etc.) to observers is mathematically represented in General Relativity mainly by means of congruences of null geodesics (light rays) and light cones (wave fronts). Given a spacetime (M, g), generally without isometries, and given world lines to represent sources and observers, one can derive relations between measurable quantitites, such as energy flux, and source properties, using the equation of geodesic deviation. In general, the focussing of light rays by gravity via Ricci and Weyl curvature causes light cones to develop caustics, consisting of points conjugate to the apex of the cone along its geodesic generators. Since light cones can be obtained as images of Legendrian maps, the local structures of their stable singularities are known from the work of Arnold. Applications to cosmology and gravitational lens theory are outlined, and open problems are mentioned.

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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and J. Ehlers