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

  • Volker Perlick

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

Table of contents

  1. Front Matter
    Pages I-X
  2. From Maxwell’s equations to ray optics

  3. A mathematical framework for ray optics

  4. Back Matter
    Pages 211-220

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.


EFE Fermat's Principle Graviational Lensing Gravity Hamiltonian Dynamics Optics Ray Optics Redshift Formula Relativity Spacetime Geometry general relativity

Authors and affiliations

  • Volker Perlick
    • 1
  1. 1.Technische Universität BerlinBerlinGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66898-5
  • Online ISBN 978-3-540-46662-8
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site