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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Ehlers' lecture
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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and J. Ehlers