A new formulation of gravitational lens theory, timedelay, and Fermat's principle
Abstract
A new analytic model for the gravitational lens effect in a clumpy universe is developed to account for image amplification and time delay effects. A twodimensional vector field is used to map the path from the source, past the lens and onto the observer plane. The field is expressed as a gradient of a scalar function derived from the intervening mass distribution. The function can then be manipulated to yield the source image, the shear and local surface mass density, and the locations where new images will appear, i.e., at the minima, maxima, and saddle points of the surface, which is described geometrically. The difference in values of the image points is the time delay between the images, although the actual light travel time through the lens deflection is a constant, as predicted by Fermat's theory.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1985
 Bibcode:
 1985A&A...143..413S
 Keywords:

 Astronomical Models;
 Big Bang Cosmology;
 Fermat Principle;
 Gravitational Lenses;
 Time Lag;
 Galaxies;
 Light Transmission;
 Quasars;
 Universe;
 Wave Diffraction;
 Astrophysics