Gravitation Waves In Einstein's Theory
by V.D. Zakharov /
1973 / English / PDF
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This book is an up-to-date review of work on gravitational waves in general relativity. Its central theme is the exposition of rigorous approaches to the problem, principally the definitions and criteria for distinguishing wavelike gravitational fields from other solutions of Einstein's equations.
The introductory chapter (Chapter 1) contains a review of approximation methods. The mathematical apparatus required for setting up the problem of rigorous (generally covariant) wave criteria — Cauchy's problem for gravitational equations and the Petrov classification of gravitational fields —is given in Chapters 2 and 3. Chapters 4-8 describe the well-known generally covariant criteria for gravitational waves of Pirani, Bell, Lichnerowicz, Zel'manov et al.
Related to these is Chapter 12, which is devoted to the chrono-metrically invariant analysis of gravitational-inertial waves. Chapter 9 deals with the theory of propagation of gravitational waves and their classification according to the nature of the wave front (plane and spherical waves). Chapter 10 discusses the special case of spaces with plane gravitational waves, more specifically spaces that admit of an absolutely parallel vector field. Chapter 11 reviews work on the asymptotic behavior of wavelike gravitational fields generated by insular distributions of sources, while the last chapter gives a brief review of the problem of experimental detection of gravitational waves and of the basic results arrived at experimentally to date. Bibliography comprising 465 entries.
