ISBN: 3-540-66898-5
TITLE: Ray Optics, Fermat's Principle, and Applications to General Relativity
AUTHOR: Perlick, Volker
TOC:

Part I. From Maxwell's equations to ray optics
1. Introduction to Part I 3
1.1 A brief guide to the literature 3
1.2 Assumptions and notations 5
2. Light propagation in linear dielectric and permeable media 7
2.1 Maxwell's equations in linear dielectric and permeable media 7
2.2 Approximate-plane-wave families 14
2.3 Asymptotic solutions of Maxwell's equations 17
2.4 Derivation of the eikonal equation and transport equations 19
2.5 Discussion of the eikonal equation 24
2.6 Discussion of transport equations and the introduction of rays 31
2.7 Ray optics as an approximation scheme 36
3. Light propagation in other kinds of media 43
3.1 Methodological remarks on dispersiv e media 44
3.2 Light propagation in a non-magnetized plasma 46
Part II. A mathematical frameworkfor ray optics
4. Introduction to Part II 61
4.1 A brief guide to the literature 61
4.2 Assumptions and notations 63
5. Ray-optical structures on arbitrary manifolds 67
5.1 Definition and basic properties of ray-optical structures 67
5.2 Regularity notions for ray-optical structures 76
5.3 Symmetries of ray-optical structures 82
5.4 Dilation-inv ariant ray-optical structures 87
5.5 Eikonal equation 92
5.6 Caustics 100
6. Ray-optical structures on Lorentzian manifolds 111
6.1 The v acuum ray-optical structure 111
6.2 Observ er fields, frequency, and redshift 113
6.3 Isotropic ray-optical structures 120
6.4 Light bundles in isotropic media 123
6.5 Stationary ray-optical structures 131
6.6 Stationary ray optics in v acuum and in simple media 141
7. Variational principles for rays 149
7.1 The principle of stationary action: The general case 149
7.2 The principle of stationary action: The strongly regular case 154
7.3 Fermat's principle 156
7.4 A Hilbert manifold setting for v ariational problems 165
7.5 A Morse theory for strongly hyperregular ray-optical structures 168
8. Applications 183
8.1 Doppler effect, aberration, and drag effect in isotropic media 183
8.2 Light rays in a uniformly accelerated medium on Minkowski space 190
8.3 Light propagation in a plasma on Kerr spacetime 193
8.4 Grav itational lensing 199
References 211
END
