Singularity Theory and Gravitational Lensing
Authors: Petters, Arlie O., Levine, Harold, Wambsganss, Joachim
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This monograph, unique in the literature, is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing.
Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Among the lensing topics discussed are multiple quasars, giant luminous arcs, Einstein rings, the detection of dark matter and planets with lensing, time delays and the age of the universe (Hubble’s constant), microlensing of stars and quasars.
The main part of the bookPart IIIemploys the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation and solve certain key lensing problems. Results are published here for the first time.
Mathematical topics discussed: Morse theory, Whitney singularity theory, Thom catastrophe theory, Mather stability theory, Arnold singularity theory, and the Euler characteristic via projectivized rotation numbers. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lens images, lensed image magnification, magnification cross sections, and lensing by singular and nonsingular deflectors.
Examples, illustrations, bibliography and index make this a suitable text for an undergraduate/graduate course, seminar, or independent these project on gravitational lensing. The book is also an excellent reference text for professional mathematicians, mathematical physicists, astrophysicists, and physicists.
 Reviews

"The time is ripe for a comprehensive volume explaining gravitational lensing to mathematicians and reviewing relevant singularity theory for astrophysicists. This is such a book. [It] . . . is accessible and attractive, . . . ranging widely through the history, physics and mathematics to paint a full picture of this . . . theory. This most attractively presented book summarizes current mathematical methods in the field and sets the stage for further exciting developments . . . A collaboration between a mathematical physicist, a mathematician, and a physicist, it has something for everybody."
—Mathematical Reviews
"This is a welldeveloped monograph on gravitational lensing both from the observational and from the mathematical points of view. However, also independent of the present interest in gravitational lensing, this book is a good source for several types of singularity theories . . . index and bibliography are very well done."
—Zentralblatt Math
"The rather voluminous monograph to be reviewed here covers both astrophysical and mathematicsl aspects of gravitational lensing. The scientific backgrohnd of the three authors guarantees that they are the right persons for such an enterprise. Arlie Petters is one of very few scientists who are competent in mathematics as well as in astrophysics. His coauthors are a pure astrophysicist and a pure matheamtician: Joachim Wambsganss is aleading expert on gravitational lensing as a tool in astrophysics and Harold Levine has made important contributions to the theory of signularities of maps in the 1960s. . . "It is not much of an exaggeration to say that large parts of this monograph can serve as a selfcontained matheamtics textbook on the theory of singularites of maps and related subjects, and even a particularly wellwritten one. So I would not hesitate to recommend it to pure matheamticians who will find a fine exposistion of a subject from their field, along with applicaions to astrophysics which should be very well readable for them. I also recommend the book to pure astrophysicists, because it contains a lot of material which has a high atrophysical relevance. . . If one compares to tbook by Petters, Leven and Wambsganss with the earlier mongraph on gravtiational lenses by Schneider, Ehlers and Falco, one finds that there is not very much overlap. The two books rather complement each other."
Gen. Relativ. Gravit.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Singularity Theory and Gravitational Lensing
 Authors

 Arlie O. Petters
 Harold Levine
 Joachim Wambsganss
 Series Title
 Progress in Mathematical Physics
 Series Volume
 21
 Copyright
 2001
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9781461201458
 DOI
 10.1007/9781461201458
 Hardcover ISBN
 9780817636685
 Softcover ISBN
 9781461266334
 Series ISSN
 15449998
 Edition Number
 1
 Number of Pages
 XXV, 603
 Topics