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Tables of Contents for Gravitational Lenses
Chapter/Section Title
Page #
Page Count
Introduction
1
25
Historical remarks
1
10
Before 1919
1
2
The period 1919--1937
3
3
The period 1963--1979
6
3
Post-1979
9
2
Outline of the book
11
10
Remarks about notation
21
4
Basic facts and the observational situation
25
66
The Schwarzschild lens
25
4
The general lens
29
4
The magnification factor
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
Doubles
48
12
Triples
60
4
Quadruples
64
7
Additional candidates
71
1
Arcs
72
5
Rings
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
Fermat's principle
100
4
Geometry of ray bundles
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
Generalizations
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
Cusps
192
5
Whitney's theorem. Singularities of generic lens maps
197
1
Stable singularities of one-parameter families of lens mappings; metamorphoses
198
17
Umbilics
199
4
Swallowtails
203
4
Lips and beak-to-beaks
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
Simple lens models
229
52
Axially symmetric lenses
230
19
General properties
230
9
The Schwarzschild lens
239
1
Disks as lenses
240
3
The singular isothermal sphere
243
1
A family of lens models for galaxies
244
3
A uniform ring
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
The two point-mass lens
261
5
Two equal point masses
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
Elliptical isopotentials
268
3
A practical approach to (nearly) elliptical lenses
271
3
Marginal lenses
274
3
Generic properties of ``elliptical lenses''
277
4
Evolution of the caustic structure
277
1
Imaging properties
278
3
Multiple light deflection
281
14
The multiple lens-plane theory
282
6
The lens equation
282
3
The magnification matrix
285
2
Particular cases
287
1
Time delay and Fermat's principle
288
3
The generalized quadrupole lens
291
4
Numerical methods
295
14
Roots of one-dimensional equations
296
2
Images of extended sources
298
1
Interactive methods for model fitting
299
1
Grid search methods
300
2
Transport of images
302
1
Ray shooting
303
4
Constructing lens and source models from resolved images
307
2
Statistical gravitational lensing: General considerations
309
62
Cross-sections
310
10
Multiple image cross-sections
311
2
Magnification cross-sections
313
7
The random star field
320
24
Probability distribution for the deflection
322
6
Shear and magnification
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
Statistics over sources
364
2
Maximum probabilities
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
Lens surveys
401
3
QSO--galaxy associations
404
15
Observational challenges
404
3
Mathematical formulation of the lensing problem
407
1
Maximal overdensity
408
3
Lens models
411
4
Relation to observations
415
4
Microlensing: Astrophysical discussion
419
16
Lens-induced variability
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
Theoretical analysis
435
9
Observational hints of amplification bias
444
3
QSO--galaxy associations revisited
447
1
Distortion of images
448
5
Lensing of supernovae
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
Introduction
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
Additional applications
501
12
The size of QSO absorption line systems
501
3
Scanning of the source by caustics
504
4
The parallax effect
508
1
Cosmic strings
509
2
Upper limits to the mass of some QSOs
511
1
Gravitational lensing and superluminal motion
512
1
Miscellaneous topics
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