Fermat's principle, caustics, and the classification of gravitational lens images

Details Fermat's principle, caustics, and the classification of gravitational lens images Fermat's principle, caustics, and the classification of gravitational lens images

Nov 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986apj...310..568b&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 310, Nov. 15, 1986, p. 568-582.

Physics

Optics

268

Caustics (Optics), Fermat Principle, Gravitational Lenses, Quasars, Catastrophe Theory, Cusps (Mathematics), Dark Matter, Density Distribution, Elliptical Galaxies, Galactic Clusters

Scientific paper

A scalar description of gravitational lensing based on Fermat's principle is described. The lensing mass is assumed to be confined to a single plane between the source and the observer, and a time delay is associated with each position in the sky of a potential image. The extrema of this time surface then give the true positions of the images. A topological classification of image configurations is presented, and the results are generalized to cases of three and five-image lensing geometries. A computer-graphical approach to the study of lensing by model galaxies and clusters is described, and the design of a simple optical apparatus which could be used for fast modelling of image geometries is outlined. The connection between the Fermat approach and the classical theory of caustics and the more recent general theory of catastrophies is developed. The extension of the results to multiple scattering is considered.

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