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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 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 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.

Differential geometry. Global analysis --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Differential geometry. --- Astrophysics. --- Mathematical Methods in Physics. --- Applications of Mathematics. --- Differential Geometry. --- Astrophysics and Astroparticles. --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Differential geometry --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics

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The theory, observations, and applications of gravitational lensing constitute one of the most rapidly growing branches of astrophysics. The gravitational deflection of light generated by mass concentrations along a light path produces magnification, multiplicity, and distortion of images and delays photon propagation from one line of sight relative to another. The huge amount of scientific work on gravitational lensing produced over the last decade has clearly revealed its already substantial and wide impact and its potential for future astrophysical applications. The up-to-date contributions in this book are based on the lecture notes of the 33rd Saas-Fee Advanced Course of the Swiss Society of Astronomy and Astrophysics, entitled Gravitational Lensing: Strong, Weak, and Micro. The book comprises four complementary parts, written by leading experts in the field, constituting a genuine textbook about gravitational lensing: ¢ Peter Schneider - Part 1: Introduction to Gravitational Lensing and Cosmology ¢ Christopher Kochanek - Part 2: Strong Gravitational Lensing ¢ Peter Schneider - Part 3: Weak Gravitational Lensing ¢ Joachim Wambsganss - Part 4: Gravitational Microlensing Students and researchers alike will benefit from this comprehensive presentation of the astrophysical and astronomical aspects of gravitational lensing.

Space research --- Cosmology --- Astrophysics --- Theory of relativity. Unified field theory --- astrofysica --- relativiteitstheorie --- ruimte (astronomie) --- kosmologie

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• Reference Manager
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The theory, observations, and applications of gravitational lensing constitute one of the most rapidly growing branches of astrophysics. The gravitational deflection of light generated by mass concentrations along a light path produces magnification, multiplicity, and distortion of images and delays photon propagation from one line of sight relative to another. The huge amount of scientific work on gravitational lensing produced over the last decade has clearly revealed its already substantial and wide impact and its potential for future astrophysical applications. The up-to-date contributions in this book are based on the lecture notes of the 33rd Saas–Fee Advanced Course of the Swiss Society of Astronomy and Astrophysics, entitled Gravitational Lensing: Strong, Weak, and Micro. The book comprises four complementary parts, written by leading experts in the field, constituting a genuine textbook about gravitational lensing: • Peter Schneider – Part 1: Introduction to Gravitational Lensing and Cosmology • Christopher Kochanek – Part 2: Strong Gravitational Lensing • Peter Schneider – Part 3: Weak Gravitational Lensing • Joachim Wambsganss – Part 4: Gravitational Microlensing Students and researchers alike will benefit from this comprehensive presentation of the astrophysical and astronomical aspects of gravitational lensing.

Gravitational lenses --- Lenses --- Astronomy. --- Astrophysics and Astroparticles. --- Astronomy, Astrophysics and Cosmology. --- Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Astronomy, Observations and Techniques. --- Gravitational lenses. --- Astrophysics. --- Gravitation. --- Observations, Astronomical. --- Astronomy—Observations. --- Astronomical observations --- Observations, Astronomical --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Astronomy --- Deism --- Metaphysics --- Astronomical physics --- Cosmic physics --- Properties