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This monograph 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. Part III employs the ideas and results of singularity
theory to put gravitational lensing on a rigorous mathematical
foundation.
The observation, in 1919 by A.S. Eddington and collaborators, of
the gra- tational de?ection of light by the Sun proved one of the
many predictions of Einstein's Theory of General Relativity: The
Sun was the ?rst example of a gravitational lens. In 1936, Albert
Einstein published an article in which he suggested - ing stars as
gravitational lenses. A year later, Fritz Zwicky pointed out that
galaxies would act as lenses much more likely than stars, and also
gave a list of possible applications, as a means to determine the
dark matter content of galaxies and clusters of galaxies. It was
only in 1979 that the ?rst example of an extragalactic
gravitational lens was provided by the observation of the distant
quasar QSO 0957+0561, by D. Walsh, R.F. Carswell, and R.J. Weymann.
A few years later, the ?rst lens showing images in the form of arcs
was detected. The theory, observations, and applications of
gravitational lensing cons- tute one of the most rapidly growing
branches of astrophysics. The gravi- tional de?ection of light
generated by mass concentrations along a light path
producesmagni?cation,multiplicity,anddistortionofimages,anddelaysp-
ton propagation from one line of sight relative to another. The
huge amount of scienti?c work produced over the last decade on
gravitational lensing has clearly revealed its already substantial
and wide impact, and its potential for future astrophysical
applications.
The observation, in 1919 by A.S. Eddington and collaborators, of
the gra- tational de?ection of light by the Sun proved one of the
many predictions of Einstein's Theory of General Relativity: The
Sun was the ?rst example of a gravitational lens. In 1936, Albert
Einstein published an article in which he suggested - ing stars as
gravitational lenses. A year later, Fritz Zwicky pointed out that
galaxies would act as lenses much more likely than stars, and also
gave a list of possible applications, as a means to determine the
dark matter content of galaxies and clusters of galaxies. It was
only in 1979 that the ?rst example of an extragalactic
gravitational lens was provided by the observation of the distant
quasar QSO 0957+0561, by D. Walsh, R.F. Carswell, and R.J. Weymann.
A few years later, the ?rst lens showing images in the form of arcs
was detected. The theory, observations, and applications of
gravitational lensing cons- tute one of the most rapidly growing
branches of astrophysics. The gravi- tional de?ection of light
generated by mass concentrations along a light path
producesmagni?cation,multiplicity,anddistortionofimages,anddelaysp-
ton propagation from one line of sight relative to another. The
huge amount of scienti?c work produced over the last decade on
gravitational lensing has clearly revealed its already substantial
and wide impact, and its potential for future astrophysical
applications.
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
book---Part III---employs 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 lensed
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 thesis
project on gravitational lensing. The book is also an excellent
reference text for professional mathematicians, mathematical
physicists, astrophysicists, and physicists.
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