Fermat's Principle, Caustics, and the Classification of Gravitational Lens Images
Abstract
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 fiveimage lensing geometries. A computergraphical 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1986
 DOI:
 10.1086/164709
 Bibcode:
 1986ApJ...310..568B
 Keywords:

 Caustics (Optics);
 Fermat Principle;
 Gravitational Lenses;
 Quasars;
 Catastrophe Theory;
 Cusps (Mathematics);
 Dark Matter;
 Density Distribution;
 Elliptical Galaxies;
 Galactic Clusters;
 Astrophysics;
 GALAXIES: CLUSTERING;
 GRAVITATION;
 QUASARS;
 RELATIVITY