Gravitational Lenses (Paperback)

1. Introduction.- 1.1 Historical remarks.- 1.1.1 Before 1919.- 1.1.2 The period 1919-1937.- 1.1.3 The period 1963-1979.- 1.1.4 Post-1979.- 1.2 Outline of the book.- 1.3 Remarks about notation.- 2. Basic facts and the observational situation.- 2.1 The Schwarzschild lens.- 2.2 The general lens.- 2.3 The magnification factor.- 2.4 Observing gravitational lens systems.- 2.4.1 Expectations for point sources..- 2.4.2 Expectations for extended sources.- 2.5 Known gravitational lens systems.- 2.5.1 Doubles.- 2.5.2 Triples.- 2.5.3 Quadruples.- 2.5.4 Additional candidates.- 2.5.5 Arcs.- 2.5.6 Rings.- 2.5.7 A rapidly growing list of candidates.- 2.5.8 Speculations on other gravitational lens systems.- 2.5.9 Gravitational lenses and cosmology.- 3. Optics in curved spacetime.- 3.1 The vacuum Maxwell equations.- 3.2 Locally approximately plane waves.- 3.3 Fermat's principle.- 3.4 Geometry of ray bundles.- 3.4.1 Ray systems and their connection vectors.- 3.4.2 Optical scalars and their transport equations.- 3.5 Distances based on light rays. Caustics.- 3.6 Luminosity, flux and intensity.- 4. Derivation of the lens equation.- 4.1 Einstein's gravitational field equation.- 4.2 Approximate metrics of isolated, slowly moving, non-compact matter distributions.- 4.3 Light deflection by quasistationary, isolated mass distributions.- 4.4 Summary of Friedmann-Lemaitre cosmological models.- 4.5 Light propagation and redshift-distance relations in homogeneous and inhomogeneous model universes.- 4.5.1 Flux conservation and the focusing theorem.- 4.5.2 Redshift-distance relations.- 4.5.3 The Dyer-Roeder equation.- 4.6 The lens mapping in cosmology.- 4.7 Wave optics in lens theory.- 5. Properties of the lens mapping.- 5.1 Basic equations of the lens theory.- 5.2 Magnification and critical curves.- 5.3 Time delay and Fermat's principle.- 5.4 Two general theorems about gravitational lensing.- 5.4.1 The case of a single lens plane.- 5.4.2 Generalizations.- 5.4.3 Necessary and sufficient conditions for multiple imaging.- 5.5 The topography of time delay (Fermat) surfaces.- 6. Lensing near critical points.- 6.1 The lens mapping near ordinary images.- 6.2 Stable singularities of lens mappings.- 6.2.1 Folds. Rules for truncating Taylor expansions.- 6.2.2 Cusps.- 6.2.3 Whitney's theorem. Singularities of generic lens maps.- 6.3 Stable singularities of one-parameter families of lens mappings; metamorphoses.- 6.3.1 Umbilics.- 6.3.2 Swallowtails.- 6.3.3 Lips and beak-to-beaks.- 6.3.4 Concluding remarks about singularities.- 6.4 Magnification of extended sources near folds.- 7. Wave optics in gravitational lensing.- 7.1 Preliminaries; magnification of ordinary images.- 7.2 Magnification near isolated caustic points.- 7.3 Magnification near fold catastrophes.- 8. Simple lens models.- 8.1 Axially symmetric lenses.- 8.1.1 General properties.- 8.1.2 The Schwarzschild lens.- 8.1.3 Disks as lenses.- 8.1.4 The singular isothermal sphere.- 8.1.5 A family of lens models for galaxies.- 8.1.6 A uniform ring.- 8.2 Lenses with perturbed symmetry (Quadrupole lenses).- 8.2.1 The perturbed Plummer model.- 8.2.2 The perturbed Schwarzschild lens ('Chang-Refsdallens').- 8.3 The two point-mass lens.- 8.3.1 Two equal point masses.- 8.3.2 Two point masses with arbitrary mass ratio.- 8.3.3 Two point masses with external shear.- 8.3.4 Generalization to N point masses.- 8.4 Lenses with elliptical symmetry.- 8.4.1 Elliptical isodensity curves.- 8.4.2 Elliptical isopotentials.- 8.4.3 A practical approach to (nearly) elliptical lenses.- 8.5 Marginal lenses.- 8.6 Generic properties of "elliptical lenses".- 8.6.1 Evolution of the caustic structure.- 8.6.2 Imaging properties.- 9. Multiple light deflection.- 9.1 The multiple lens-plane theory.- 9.1.1 The lens equation.- 9.1.2 The magnification matrix.- 9.1.3 Particular cases.- 9.2 Time delay and Fermat's principle.- 9.3 The generalized quadrupole lens.- 10. Numerical methods.- 10.1 Roots of one-dimensional equations.- 10.2 Images of extended sou