Properties of the lens mapping
In this chapter we describe general properties of the lens mapping. In Sect. 5.1 the basic equations of GL theory are presented and briefly discussed. A general description of the lens mapping in the infinitesimal neighborhood of a point is given in Sect. 5.2. It leads to the concepts of magnification and critical curves and to a classification of ordinary images. In Sect. 5.3 the light-travel-time along ray bundles that correspond to GL images is determined by means of the geometry of wavefronts; this again leads to the connection between Fermat’s principle and the lens mapping. The difference in light-travel-time for different images of a source is an observable; this time delay is one of the central quantities in gravitational lensing. Two general theorems are proved in Sect. 5.4, and a classification of 3-image and 5-image topographies is presented in Sect. 5.5.
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