Gravitational Solitons Book

	Preface
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