Belinski V., Verdaguer E. Gravitational Solitons

Cambrige University Press. First published in printed format 2001. 273 p.This book gives a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein’s equations.The text begins with a detailed discussion of the extension of the inverse scattering method to the theory of gravitation, starting with pure gravity and then extending it to the coupling of gravity with the electromagnetic field. There follows a systematic review of the gravitational soliton solutions based on their symmetries. These solutions include some of the most interesting in gravitational physics, such as those describing inhomogeneous cosmological models, cylindrical waves, the collision of exact gravity waves, and the Schwarzschild and Kerr black holes.This work will equip the reader with the basic elements of the theory of gravitational solitons as well as with a systematic collection of nontrivial applications in different contexts of gravitational physics. It provides a valuable reference for researchers and graduate students in the fields of general relativity, string theory and cosmology, but will also be of interest to mathematical physicists in general.Inverse scattering technique in gravity
Outline of the ISM
The integrable ansatz in general relativity
The integration scheme
Construction of the n-soliton solution
Multidimensional spacetimeGeneral properties of gravitational solitons
The simple and double solitons
Diagonal background metrics
Topological propertiesEinstein–Maxwell fields
The Einstein–Maxwell field equations
The spectral problem for Einstein–Maxwell fields
The components g_ab and the potentials A_a
The metric component f
Einstein–Maxwell breathersCosmology: diagonal metrics from Kasner
Anisotropic and inhomogeneous cosmologies
Kasner background
Geometrical characterization of diagonal metrics
Soliton solutions in canonical coordinates
Solutions with real poles
Solutions with complex polesCosmology: nondiagonal metrics and perturbed FLRW
Nondiagonal metrics
Bianchi II backgrounds
Collision of pulse waves and soliton waves
Solitons on FLRW backgroundsCylindrical symmetry
Cylindrically symmetric spacetimes
Einstein–Rosen soliton metrics
Two polarization waves and Faraday rotationPlane waves and colliding plane waves
Overview
Plane waves
Colliding plane wavesAxial symmetry
The integration scheme
General n-soliton solution
The Kerr and Schwarzschild metrics
Asymptotic flatness of the solution
Generalized soliton solutions of the Weyl class
Tomimatsu–Sato solution