Singular null hypersurfaces in general relativity : light-like signals from violent astrophysical events /
This book presents a comprehensive and self-contained exposition of the mathematical theory of impulsive light-like signals in general relativity. Applications are provided in relativistic astrophysics, cosmology and alternative theories of gravity deduced from string theory. Cataclysmic astrophysic...
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| Format: | Electronic eBook |
| Language: | English |
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River Edge, N.J. :
World Scientific,
©2003.
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| Online Access: | CONNECT |
Table of Contents:
- Preface
- 1. Introduction. 1.1. Synge's model. 1.2. Penrose's cut and paste approach. 1.3. Generalized Lorentz transformations
- 2. General description of an impulsive light-like signal. 2.1. Distributional algorithm. 2.2. Transverse curvature algorithm. 2.3. Splitting the signal into a shell and a gravitational wave. 2.4. An example of a plane fronted light-like signal
- 3. Illustrations and implications of the Bianchi identities. 3.1. Abrupt changes in multipole moments. 3.2 Impulsive light-like signals as recoil effects: electromagnetic example. 3.3. Impulsive light-like signals as recoil effects: gravitational example. 3.4. Interaction of impulsive light-like signals with matter. 3.5. Implications of the Bianchi identities. 3.6. Theory of the detection of impulsive light-like signals
- 4. Light-like boosts of gravitating bodies. 4.1. Introduction: light-like boost of the Coulomb field. 4.2. Boosting an isolated gravitating source. 4.3. Light-like boost of the Kerr field. 4.4. Deflection of highly relativistic particles in the Kerr field. 4.5. The exceptional case of a cosmic string
- 5. Spherically symmetric null shells. 5.1. Properties and examples of non-stationary spherical null shells. 5.2. Horizon-straddling null shells. 5.3. Colliding spherical null shells. 5.4. Gravitational collapse, gravitational radiation and singularities
- 6. Collisions of plane impulsive light-like signals. 6.1. Khan-Penrose solution. 6.2. Colliding plane impulsive gravitational waves: the general case. 6.3. Plane impulsive light-like signal collisions: some non-interacting examples
- 7. Impulsive light-like signals in alternative theories of gravity. 7.1. Scalar-tensor theories of gravitation. 7.2. Einstein-Cartan theory of gravitation. 7.3. Einstein-Gauss-Bonnet theory of gravitation
- Appendix A. Notation
- Appendix B. Singular hypersurfaces: the non-null case
- Bibliography.
