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Gravitational Solitons

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Here is 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.

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Editorial Reviews

From the Publisher
"This monograph provides a valuable reference for researchers and graduate students in the field of general relativity, string theory and cosmology, but will also be of interest to mathematical physicists in general." Mathematical Reviews
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Product Details

Meet the Author

Vladimir A. Belinski studied at the Landau Institute for Theoretical Physics, where he completed his doctorate and worked until 1990. Currently he is Research Supervisor by special appointment at the National Institute for Nuclear Physics, Rome, specialising in General Relativity, Cosmology and Nonlinear Physics. He is best known for two scientific results, firstly the proof that there is an infinite curvature singularity in the general solution of Einstein equations, and the discovery of the chaotic oscillatory structure of this singularity, known as the BKL singularity (1968–75, with I. M. Khalatnikov and E. M. Lifshitz), and secondly the formulation of the Inverse Scattering Method in General Relativity and the discovery of gravitational solitons (1977–82, with V. E. Zakharov).

Enric Verdaguer received his PhD in physics from the Autonomous University of Barcelona in 1977, and has held a professorship at the University of Barcelona since 1993. He specialises in General Relativity and Quantum Field Theory in Curved Spacetimes, and pioneered the use of the Belinski-Zakharov Inverse Scattering Method in different gravitational contexts, particularly in cosmology, discovering new physical properties in gravitational solitons. Since 1991 his main research interest has been the interaction of quantum fields with gravity. He has studied the consequences of this interaction in the collision of exact gravity waves, in the evolution of cosmic strings and in cosmology. More recently he has worked in the formulation and physical consequences of stochastic semiclassical gravity.

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Table of Contents

1 Inverse scattering technique in gravity 1
1.1 Outline of ISM 1
1.2 The integrable ansatz in general relativity 10
1.3 The integration scheme 14
1.4 Construction of the n-soliton solution 17
1.5 Multidimensional spacetime 28
2 General properties of gravitational solitons 37
2.1 The simple and double solitons 37
2.2 Diagonal background metrics 45
2.3 Topological properties 48
3 Einstein-Maxwell fields 60
3.1 The Einstein-Maxwell field equations 60
3.2 The spectral problem for Einstein-Maxwell fields 65
3.3 The components g[subscript ab] and the potentials A[subscript a] 69
3.4 The metric component f 82
3.5 Einstein-Maxwell breathers 84
4 Cosmology: diagonal metrics from Kasner 92
4.1 Anisotropic and inhomogeneous cosmologies 93
4.2 Kasner background 95
4.3 Geometrical characterization of diagonal metrics 96
4.4 Soliton solutions in canonical coordinates 101
4.5 Solutions with real poles 106
4.6 Solutions with complex poles 115
5 Cosmology: nondiagonal metrics and perturbed FLRW 133
5.1 Nondiagonal metrics 133
5.2 Bianchi II backgrounds 140
5.3 Collision of pulse waves and soliton waves 142
5.4 Solitons on FLRW backgrounds 148
6 Cylindrical symmetry 169
6.1 Cylindrically symmetric spacetimes 169
6.2 Einstein-Rosen soliton metrics 172
6.3 Two polarization waves and Faraday rotation 178
7 Plane waves and colliding plane waves 183
7.1 Overview 183
7.2 Plane waves 185
7.3 Colliding plane waves 194
8 Axial symmetry 213
8.1 The integration scheme 214
8.2 General n-soliton solution 216
8.3 The Kerr and Schwarzschild metrics 220
8.4 Asymptotic flatness of the solution 224
8.5 Generalized soliton solutions of the Weyl class 227
8.6 Tomimatsu-Sato solution 238
Bibliography 241
Index 253
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