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Tables of Contents for Ray Optics, Fermat's Principle, and Applications to General Relativity
Chapter/Section Title
Page #
Page Count
Part I. From Maxwell's equations to ray optics
Introduction to Part I
3
4
A brief guide to the literature
3
2
Assumptions and notations
5
2
Light propagation in linear dielectric and permeable media
7
36
Maxwell's equations in linear dielectric and permeable media
7
7
Approximate-plane-wave families
14
3
Asymptotic solutions of Maxwell's equations
17
2
Derivation of the eikonal equation and transport equations
19
5
Discussion of the eikonal equation
24
7
Discussion of transport equations and the introduction of rays
31
5
Ray optics as an approximation scheme
36
7
Light propagation in other kinds of media
43
18
Methodological remarks on dispersive media
44
2
Light propagation in a non-magnetized plasma
46
15
Part II. A mathematical framework for ray optics
Introduction to Part II
61
6
A brief guide to the literature
61
2
Assumptions and notations
63
4
Ray-optical structures on arbitrary manifolds
67
44
Definition and basic properties of ray-optical structures
67
9
Regularity notions for ray-optical structures
76
6
Symmetries of ray-optical structures
82
5
Dilation-invariant ray-optical structures
87
5
Eikonal equation
92
8
Caustics
100
11
Ray-optical structures on Lorentzian manifolds
111
38
The vacuum ray-optical structure
111
2
Observer fields, frequency, and redshift
113
7
Isotropic ray-optical structures
120
3
Light bundles in isotropic media
123
8
Stationary ray-optical structures
131
10
Stationary ray optics in vacuum and in simple media
141
8
Variational principles for rays
149
34
The principle of stationary action: The general case
149
5
The principle of stationary action: The strongly regular case
154
2
Fermat's principle
156
9
A Hilbert manifold setting for variational problems
165
3
A Morse theory for strongly hyperregular ray-optical structures
168
15
Applications
183
28
Doppler effect, aberration, and drag effect in isotropic media
183
7
Light rays in a uniformly accelerated medium on Minkowski space
190
3
Light propagation in a plasma on Kerr spacetime
193
6
Gravitational lensing
199
12
References
211