Ray Optics, Fermat's Principle, and Applications to General Relativity
Edition: 1 edition
Publisher: Springer
Published: March 15, 2000
Language: eng
Format: Hardcover
Number of pages: 230
ISBN-13: 9783540668985
Subjects: Astrophysics; Mathematics for scientists & engineers; Optics (light); Science/Mathematics; Mathematical models; General Relativity Theory; Geometric Optics; Science; Relativity; Maxwell equations; Astrophysics & Space Science; General; Optics; Fermat's Principle; Graviational Lensing; Hamiltonian Dynamics; Medical-General; Ray Optics; Redshift Formula; Transmission; General relativity (Physics); Light
First sentence: In Part I we recapitulate the general ideas of how to derive the laws of ray optics from Maxwell's equations.
Description: 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.