Ray Optics, Fermat's Principle, and Applications to General Relativity / Edition 1

by Volker Perlick

Overview

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.

Product Details

ISBN-13:	9783540668985
Publisher:	Springer Berlin Heidelberg
Publication date:	03/15/2000
Series:	Lecture Notes in Physics Monographs , #61
Edition description:	2000
Pages:	222
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

From Maxwell’s equations to ray optics.- to Part I.- Light propagation in linear dielectric and permeable media.- Light propagation in other kinds of media.- A mathematical framework for ray optics.- to Part II.- Ray-optical structures on arbitrary manifolds.- Ray-optical structures on Lorentzian manifolds.- Variational principles for rays.- Applications.