# Ray Optics, Fermat's Principle, And Applications To General Relativity

by Volker Perlick /
2000 / English / PDF

16.9 MB Download

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.

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.