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This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods.
The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields.
The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.
Table of Contents
- Selected Solutions of Einstein's Field Equations: Their Role in General Relativity and Astrophysics
- 1 Introduction and a Few Excursions
- 2 The Schwarzschild Solution
- 3 The ReissnerNordström Solution
- 4 The Kerr Metric
- 5 Black Hole Uniqueness and Multi-black Hole Solutions
- 6 On Stationary Axisymmetric Fields and Relativistic Disks
- 7 Taub-NUT Space
- 8 Plane Waves and Their Collisions
- 9 Cylindrical Waves
- 10 On the RobinsonTrautman Solutions
- 11 The Boost-Rotation Symmetric Radiative Spacetimes
- 12 The Cosmological Models
- 13 Concluding Remarks
- The Cauchy Problem for the Einstein Equations
- 1 Introduction
- 2 Basic Observations and Concepts
- 3 PDE Techniques
- 4 Reductions
- 5 Local Evolution
- 6 Outlook
- Post-Newtonian Gravitational Radiation
- 1 Introduction
- 2 Multipole Decomposition
- 3 Source Multipole Moments
- 4 Post-Minkowskian Approximation
- 5 Radiative Multipole Moments
- 6 Post-Newtonian Approximation
- 7 Point-Particles
- 8 Conclusion
- Duality and Hidden Symmetries in Gravitational Theories
- 1 Introduction
- 2 Electromagnetic Duality
- 3 Duality in KaluzaKlein Theories
- 4 Geroch Group
- 5 Stationary Black Holes
- 6 Acknowledgments
- 7 Non-linear sigma-Models and Symmetric Spaces
- 8 Structure of the Lie Algebra
- Time-Independent Gravitational Fields
- 1 Introduction
- 2 Field Equations
- 3 Far Fields
- 4 Global Rotating Solutions
- 5 Global Non-rotating Solutions
- Gravitational Lensing from a Geometric Viewpoint
- 1 Introduction
- 2 Some Basic Notions of Spacetime Geometry
- 3 Gravitational Lensing in Arbitrary Spacetimes
- 4 Gravitational Lensing in Globally Hyperbolic Spacetimes
- 5 Gravitational Lensing in Asymptotically Simple and Empty Spacetimes
Readership:
Researchers and graduate students
Springer Berlin, 2000, 434 S.
106,95 Euro
Hardcover
ISBN: 978-3-540-67073-5
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