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

  • Book
  • © 2000

Overview

Authors:
  1. Volker Perlick

    1. Technische Universität Berlin, Berlin, Germany

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  • There exists no text on relativistic ray optics in book form although the theory is heavily used in astrophysical models
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 61)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  3. A mathematical framework for ray optics

    1. Introduction to Part II

      Pages 61-65

    2. Ray-optical structures on arbitrary manifolds

      Pages 67-109

    3. Ray-optical structures on Lorentzian manifolds

      Pages 111-147

    4. Variational principles for rays

      Pages 149-181

    5. Applications

      Pages 183-210

  4. Back Matter

    Pages 211-220
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Keywords

About this book

This book is about the mathematical theory of light propagation in media on general-relativistic spacetimes. The first part discusses the transition from Maxwell's equations to ray optics. The second part establishes a general mathematical framework for treating ray optics as a theory in its own right, making extensive use of the Hamiltonian formalism. This part also includes a detailed discussion of variational principles (i.e., various versions of Fermat's principle) for light rays in general-relativistic media. Some applications, e.g. to gravitational lensing, are worked out. The reader is assumed to have some basic knowledge of general relativity and some familiarity with differential geometry. Some of the results are published here for the first time, e.g. a general-relativistic version of Fermat's principle for light rays in a medium that has to satisfy some regularity condition only.

Authors and Affiliations

  • Technische Universität Berlin, Berlin, Germany

    Volker Perlick

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