Singularity Theory and Gravitational Lensing

This monograph addresses several fundamental mathematical and physical issues in gravitational lensing. It serves both as an introduction to the field and as a late-1990s, illustrated, exposition of important aspects of lensing.

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This monograph addresses several fundamental mathematical and physical issues in gravitational lensing. Mathematical topics include a study of the stable features of maps arising in lensing, the local and global geometry of caustics due to gravitational lenses, the magnification and multiple imaging of lensed light sources, and multi-plane lensing by singular and nonsingular deflectors. Some of the (astro-) physical topics are Einstein rings and Giant Luminous Arcs, time delay and Hubble's constant, microlensing of stars and quasars and the detection of dark matter and planets with lensing. The authors employ the ideas and results of singularity theory not only to treat these topics, but also to put gravitational lensing on a rigorous mathematical foundation. The mathematics is at a level of generality that preserves the essential physical ideas and facilitates a simple, unified presentation of the theory. The book should be accessible and of interest to mathematicians and physical scientists, including graduate students. It serves both as an introduction to the field and as a late-1990s, illustrated, exposition of important aspects of lensing.