Book contents
- Frontmatter
- Contents
- Preface
- 1 Inverse scattering technique in gravity
- 2 General properties of gravitational solitons
- 3 Einstein–Maxwell fields
- 4 Cosmology: diagonal metrics from Kasner
- 5 Cosmology: nondiagonal metrics and perturbed FLRW
- 6 Cylindrical symmetry
- 7 Plane waves and colliding plane waves
- 8 Axial symmetry
- Bibliography
- Index
2 - General properties of gravitational solitons
Published online by Cambridge University Press: 17 August 2009
- Frontmatter
- Contents
- Preface
- 1 Inverse scattering technique in gravity
- 2 General properties of gravitational solitons
- 3 Einstein–Maxwell fields
- 4 Cosmology: diagonal metrics from Kasner
- 5 Cosmology: nondiagonal metrics and perturbed FLRW
- 6 Cylindrical symmetry
- 7 Plane waves and colliding plane waves
- 8 Axial symmetry
- Bibliography
- Index
Summary
In this chapter we give some general properties of the gravitational soliton solutions. The simplest soliton solutions, those with fewer poles, are studied in general and the pole fusion limit is described in section 2.1. In section 2.2 the case of a diagonal, but otherwise arbitrary, background metric is considered. It turns out that the integration of the spectral equations for the background solution in this case reduces to quadratures and the one- and two-soliton solutions can be given in general. Section 2.3 is devoted to the characterization of the gravitational solitons by some of the properties that solitons have in nongravitational physics. We see that the properties of the solitons do not always have a correspondence in the gravitational case. But under some restrictions some of these properties such as the topological charge can be identified. Thus, we can identify gravitational solitons and antisolitons, and, in particular, a remarkable solution that is the gravitational analogue of the sine-Gordon breather.
The simple and double solitons
Here we give a suitable form to the one- and two-soliton solutions, the simplest particular cases of the multisoliton solution described in section 1.4, and investigate some of their general properties. Everywhere in this chapter we deal only with physical values of the metric coefficients which obey the full system of Einstein equations (1.38) – (1.42) and, for simplicity, we omit the label ‘ph’ in these coefficients.
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- Chapter
- Information
- Gravitational Solitons , pp. 37 - 59Publisher: Cambridge University PressPrint publication year: 2001