|
|
1 | (25) |
|
|
1 | (10) |
|
|
1 | (2) |
|
|
3 | (3) |
|
|
6 | (3) |
|
|
9 | (2) |
|
|
11 | (10) |
|
|
21 | (4) |
|
Basic facts and the observational situation |
|
|
25 | (66) |
|
|
25 | (4) |
|
|
29 | (4) |
|
|
33 | (8) |
|
Observing gravitational lens systems |
|
|
41 | (6) |
|
Expectations for point sources |
|
|
42 | (4) |
|
Expectations for extended sources |
|
|
46 | (1) |
|
Known gravitational lens systems |
|
|
47 | (44) |
|
|
48 | (12) |
|
|
60 | (4) |
|
|
64 | (7) |
|
|
71 | (1) |
|
|
72 | (5) |
|
|
77 | (7) |
|
A rapidly growing list of candidates |
|
|
84 | (1) |
|
Speculations on other gravitational lens systems |
|
|
84 | (5) |
|
Gravitational lenses and cosmology |
|
|
89 | (2) |
|
Optics in curved spacetime |
|
|
91 | (28) |
|
The vacuum Maxwell equations |
|
|
91 | (2) |
|
Locally approximately plane waves |
|
|
93 | (7) |
|
|
100 | (4) |
|
|
104 | (6) |
|
Ray systems and their connection vectors |
|
|
104 | (2) |
|
Optical scalars and their transport equations |
|
|
106 | (4) |
|
Distances based on light rays. Caustics |
|
|
110 | (5) |
|
Luminosity, flux and intensity |
|
|
115 | (4) |
|
Derivation of the lens equation |
|
|
119 | (38) |
|
Einstein's gravitational field equation |
|
|
119 | (2) |
|
Approximate metrics of isolated, slowly moving, non-compact matter distributions |
|
|
121 | (2) |
|
Light deflection by quasistationary, isolated mass distributions |
|
|
123 | (4) |
|
Summary of Friedmann-Lemaitre cosmological models |
|
|
127 | (5) |
|
Light propagation and redshift-distance relations in homogeneous and inhomogeneous model universes |
|
|
132 | (11) |
|
Flux conservation and the focusing theorem |
|
|
132 | (2) |
|
Redshift--distance relations |
|
|
134 | (3) |
|
The Dyer--Roeder equation |
|
|
137 | (6) |
|
The lens mapping in cosmology |
|
|
143 | (7) |
|
Wave optics in lens theory |
|
|
150 | (7) |
|
Properties of the lens mapping |
|
|
157 | (26) |
|
Basic equations of the lens theory |
|
|
157 | (4) |
|
Magnification and critical curves |
|
|
161 | (5) |
|
Time delay and Fermat's principle |
|
|
166 | (6) |
|
Two general theorems about gravitational lensing |
|
|
172 | (5) |
|
The case of a single lens plane |
|
|
172 | (4) |
|
|
176 | (1) |
|
Necessary and sufficient conditions for multiple imaging |
|
|
177 | (1) |
|
The topography of time delay (Fermat) surfaces |
|
|
177 | (6) |
|
Lensing near critical points |
|
|
183 | (34) |
|
The lens mapping near ordinary images |
|
|
184 | (1) |
|
Stable singularities of lens mappings |
|
|
185 | (13) |
|
Folds. Rules for truncating Taylor expansions |
|
|
186 | (6) |
|
|
192 | (5) |
|
Whitney's theorem. Singularities of generic lens maps |
|
|
197 | (1) |
|
Stable singularities of one-parameter families of lens mappings; metamorphoses |
|
|
198 | (17) |
|
|
199 | (4) |
|
|
203 | (4) |
|
|
207 | (4) |
|
Concluding remarks about singularities |
|
|
211 | (4) |
|
Magnification of extended sources near folds |
|
|
215 | (2) |
|
Wave optics in gravitational lensing |
|
|
217 | (12) |
|
Preliminaries; magnification of ordinary images |
|
|
217 | (3) |
|
Magnification near isolated caustic points |
|
|
220 | (2) |
|
Magnification near fold catastrophes |
|
|
222 | (7) |
|
|
229 | (52) |
|
|
230 | (19) |
|
|
230 | (9) |
|
|
239 | (1) |
|
|
240 | (3) |
|
The singular isothermal sphere |
|
|
243 | (1) |
|
A family of lens models for galaxies |
|
|
244 | (3) |
|
|
247 | (2) |
|
Lenses with perturbed symmetry (Quadrupole lenses) |
|
|
249 | (12) |
|
The perturbed Plummer model |
|
|
252 | (3) |
|
The perturbed Schwarzschild lens (`Chang-Refsdal lens') |
|
|
255 | (6) |
|
|
261 | (5) |
|
|
261 | (3) |
|
Two point masses with arbitrary mass ratio |
|
|
264 | (1) |
|
Two point masses with external shear |
|
|
264 | (1) |
|
Generalization to N point masses |
|
|
265 | (1) |
|
Lenses with elliptical symmetry |
|
|
266 | (8) |
|
Elliptical isodensity curves |
|
|
267 | (1) |
|
|
268 | (3) |
|
A practical approach to (nearly) elliptical lenses |
|
|
271 | (3) |
|
|
274 | (3) |
|
Generic properties of ``elliptical lenses'' |
|
|
277 | (4) |
|
Evolution of the caustic structure |
|
|
277 | (1) |
|
|
278 | (3) |
|
Multiple light deflection |
|
|
281 | (14) |
|
The multiple lens-plane theory |
|
|
282 | (6) |
|
|
282 | (3) |
|
|
285 | (2) |
|
|
287 | (1) |
|
Time delay and Fermat's principle |
|
|
288 | (3) |
|
The generalized quadrupole lens |
|
|
291 | (4) |
|
|
295 | (14) |
|
Roots of one-dimensional equations |
|
|
296 | (2) |
|
Images of extended sources |
|
|
298 | (1) |
|
Interactive methods for model fitting |
|
|
299 | (1) |
|
|
300 | (2) |
|
|
302 | (1) |
|
|
303 | (4) |
|
Constructing lens and source models from resolved images |
|
|
307 | (2) |
|
Statistical gravitational lensing: General considerations |
|
|
309 | (62) |
|
|
310 | (10) |
|
Multiple image cross-sections |
|
|
311 | (2) |
|
Magnification cross-sections |
|
|
313 | (7) |
|
|
320 | (24) |
|
Probability distribution for the deflection |
|
|
322 | (6) |
|
|
328 | (2) |
|
Inclusion of external shear and smooth matter density |
|
|
330 | (4) |
|
Correlated deflection probability |
|
|
334 | (3) |
|
Spatial distribution of magnifications |
|
|
337 | (7) |
|
Probabilities in a clumpy universe |
|
|
344 | (4) |
|
Light propagation in inhomogeneous universes |
|
|
348 | (18) |
|
Statistics for light rays |
|
|
350 | (14) |
|
|
364 | (2) |
|
|
366 | (5) |
|
Statistical gravitational lensing: Applications |
|
|
371 | (96) |
|
Amplification bias and the luminosity function of QSOs |
|
|
373 | (7) |
|
Amplification bias: Preliminary discussion |
|
|
373 | (5) |
|
QSO source counts and their luminosity function |
|
|
378 | (2) |
|
Statistics of multiply imaged sources |
|
|
380 | (24) |
|
Statistics for point-mass lenses |
|
|
381 | (4) |
|
Statistics for isothermal spheres |
|
|
385 | (10) |
|
Modifications of the lens model: Symmetric lenses |
|
|
395 | (4) |
|
Modification of the lens model: Asymmetric lenses |
|
|
399 | (2) |
|
|
401 | (3) |
|
|
404 | (15) |
|
|
404 | (3) |
|
Mathematical formulation of the lensing problem |
|
|
407 | (1) |
|
|
408 | (3) |
|
|
411 | (4) |
|
|
415 | (4) |
|
Microlensing: Astrophysical discussion |
|
|
419 | (16) |
|
|
421 | (4) |
|
Microlensing in 2237 + 0305 |
|
|
425 | (4) |
|
Microlensing and broad emission lines of QSOs |
|
|
429 | (4) |
|
Microlensing and the classification of AGNs |
|
|
433 | (2) |
|
The amplification bias: Detailed discussion |
|
|
435 | (13) |
|
|
435 | (9) |
|
Observational hints of amplification bias |
|
|
444 | (3) |
|
QSO--galaxy associations revisited |
|
|
447 | (1) |
|
|
448 | (5) |
|
|
453 | (3) |
|
Further applications of statistical lensing |
|
|
456 | (11) |
|
Gravitational microlensing by the galactic halo |
|
|
456 | (4) |
|
Recurrence of γ-ray bursters |
|
|
460 | (1) |
|
Multiple imaging from an ensemble of galaxies, and the `missing lens' problem |
|
|
461 | (6) |
|
Gravitational lenses as astrophysical tools |
|
|
467 | (50) |
|
Estimation of model parameters |
|
|
468 | (15) |
|
Invariance transformations |
|
|
471 | (2) |
|
Determination of lens mass and Hubble constant |
|
|
473 | (3) |
|
Application to the 0957 + 561 system |
|
|
476 | (7) |
|
Arcs in clusters of galaxies |
|
|
483 | (18) |
|
|
483 | (2) |
|
The nearly spherical lens |
|
|
485 | (7) |
|
Analysis of the observations; arcs as astronomical tools |
|
|
492 | (6) |
|
Statistics of arcs and arclets |
|
|
498 | (3) |
|
|
501 | (12) |
|
The size of QSO absorption line systems |
|
|
501 | (3) |
|
Scanning of the source by caustics |
|
|
504 | (4) |
|
|
508 | (1) |
|
|
509 | (2) |
|
Upper limits to the mass of some QSOs |
|
|
511 | (1) |
|
Gravitational lensing and superluminal motion |
|
|
512 | (1) |
|
|
513 | (4) |
|
Lensing and the microwave background |
|
|
513 | (1) |
|
Light deflection in the Solar System |
|
|
514 | (1) |
|
Light deflection in strong fields |
|
|
514 | (3) |
References |
|
517 | (28) |
Index of Individual Objects |
|
545 | (2) |
Subject Index |
|
547 | |