Ray Optics, Fermat’s Principle, and Applications to General Relatively

Cover ......Page 1
Lecture Notes in Physics: Monographs 61 ......Page 2
Ray Optics, Fermat\'s Principle, and Applications to General Relativity ......Page 4
Preface ......Page 6
Contents ......Page 10
1.1 A brief guide to the literature ......Page 12
1.2 Assumptions and notations ......Page 14
2.1 Maxwell\'s equations in linear dielectric and permeable media ......Page 16
2.2 Approximate-plane-wave families ......Page 23
2.3 Asymptotic solutions of Maxwell\'s equations ......Page 26
2.4 Derivation of the eikonal equation and transport equations ......Page 28
2.5 Discussion of the eikonal equation ......Page 33
2.6 Discussion of transport equations and the introduction of rays ......Page 40
2.7 Ray optics as an approximation scheme ......Page 45
3. Light propagation in other kinds of media ......Page 52
3.1 Methodological remarks on dispersive media ......Page 53
3.2 Light propagation in a non-magnetized plasma ......Page 55
4.1 A brief guide to the literature ......Page 68
4.2 Assumptions and notations ......Page 70
5.1 Definition and basic properties of ray-optical structures ......Page 74
5.2 Regularity notions for ray-optical structures ......Page 83
5.3 Symmetries of ray-optical structures ......Page 89
5.4 Dilation-invariant ray-optical structures ......Page 94
5.5 Eikonal equation ......Page 99
5.6 Caustics ......Page 107
6.1 The vacuum ray-optical structure ......Page 118
6.2 Observer fields, frequency, and redshift ......Page 120
6.3 Isotropic ray-optical structures ......Page 127
6.4 Light bundles in isotropic media ......Page 130
6.5 Stationary ray-optical structures ......Page 138
6.6 Stationary ray optics in vacuum and in simple media ......Page 148
7.1 The principle of stationary action: The general case ......Page 156
7.2 The principle of stationary action: The strongly regular case ......Page 161
7.3 Fermat\'s principle ......Page 163
7.4 A Hilbert manifold setting for variational problems ......Page 172
7.5 A Morse theory for strongly hyperregular ray-optical structures ......Page 175
8.1 Doppler effect, aberration, and drag effect in isotropic media ......Page 190
8.2 Light rays in a uniformly accelerated medium on Minkowski space ......Page 197
8.3 Light propagation in a plasma on Kerr spacetime ......Page 200
8.4 Gravitational lensing ......Page 206
References ......Page 218
Index ......Page 224