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Look Inside Exact Solutions of Einstein's Field Equations

Exact Solutions of Einstein's Field Equations

2nd Edition

Part of Cambridge Monographs on Mathematical Physics

Authors:
Hans Stephani, Friedrich-Schiller-Universität, Jena, Germany
Dietrich Kramer, Friedrich-Schiller-Universität, Jena, Germany
Malcolm MacCallum, Queen Mary University of London
Cornelius Hoenselaers, Loughborough University
Eduard Herlt, Friedrich-Schiller-Universität, Jena, Germany

Date Published: October 2009
availability: Available
format: Paperback
isbn: 9780521467025

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About the Authors

A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.
- An updated and expanded edition of a classic text, containing important new methods and solutions
- Includes generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions
- A unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources
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Reviews & endorsements
"This is clearly a most valuable reference book. It comprehensively reviews known local solutions of Einstein's equation and provides a secure base for future research."
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Product details
- Edition: 2nd Edition
- Date Published: October 2009
- format: Paperback
- isbn: 9780521467025
- length: 732 pages
- dimensions: 244 x 175 x 43 mm
- weight: 1.28kg
- contains: 10 b/w illus. 50 tables
- availability: Available
Table of Contents
Preface
List of tables
Notation
1. Introduction
Part I. General Methods:
2. Differential geometry without a metric
3. Some topics in Riemannian geometry
4. The Petrov classification
5. Classification of the Ricci tensor and the energy-movement tensor
6. Vector fields
7. The Newman–Penrose and related formalisms
8. Continuous groups of transformations
isometry and homothety groups
9. Invariants and the characterization of geometrics
10. Generation techniques
Part II. Solutions with Groups of Motions:
11. Classification of solutions with isometries or homotheties
12. Homogeneous space-times
13. Hypersurface-homogeneous space-times
14. Spatially-homogeneous perfect fluid cosmologies
15. Groups G3 on non-null orbits V2. Spherical and plane symmetry
16. Spherically-symmetric perfect fluid solutions
17. Groups G2 and G1 on non-null orbits
18. Stationary gravitational fields
19. Stationary axisymmetric fields: basic concepts and field equations
20. Stationary axisymmetiric vacuum solutions
21. Non-empty stationary axisymmetric solutions
22. Groups G2I on spacelike orbits: cylindrical symmetry
23. Inhomogeneous perfect fluid solutions with symmetry
24. Groups on null orbits. Plane waves
25. Collision of plane waves
Part III. Algebraically Special Solutions:
26. The various classes of algebraically special solutions. Some algebraically general solutions
27. The line element for metrics with κ=σ=0=R11=R14=R44, Θ+iω≠0
28. Robinson–Trautman solutions
29. Twisting vacuum solutions
30. Twisting Einstein–Maxwell and pure radiation fields
31. Non-diverging solutions (Kundt's class)
32. Kerr–Schild metrics
33. Algebraically special perfect fluid solutions
Part IV. Special Methods:
34. Applications of generation techniques to general relativity
35. Special vector and tensor fields
36. Solutions with special subspaces
37. Local isometric embedding of four-dimensional Riemannian manifolds
Part V. Tables:
38. The interconnections between the main classification schemes
References
Index.
Look Inside
Authors
Hans Stephani, Friedrich-Schiller-Universität, Jena, Germany
Hans Stephani gained his diploma, Ph.D. and Habilitation at the Friedrich-Schiller-Universität Jena. He became Professor of Theoretical Physics in 1992, before retiring in 2000. He has been lecturing in theoretical physics since 1964 and has published numerous papers and articles on relativity and optics. He is also the author of four books.
Dietrich Kramer, Friedrich-Schiller-Universität, Jena, Germany
Dietrich Kramer is Professor of Theoretical Physics at the Friedrich-Schiller-Universität Jena. He graduated from this university, where he also finished his Ph.D. (1966) and Habilitation (1970). His current research concerns classical relativity. The majority of his publications are devoted to exact solutions in general relativity.
Malcolm MacCallum, Queen Mary University of London
Malcolm MacCallum is Professor of Applied Mathematics at the School of Mathematical Sciences, Queen Mary, University of London, where he is also Vice-Principal for Science and Engineering. He graduated from King's College, Cambridge and went on to complete his M.A. and Ph.D. there. His research covers general relativity and computer algebra, especially tensor manipulators and differential equations. He has published over 100 pages, review articles and books.
Cornelius Hoenselaers, Loughborough University
Cornelius Hoenselaers gained his Diploma at Technische Universität Karlsruhe, his D.Sc. at Hiroshima Daigaku and his Habilitation at Ludwig-Maximilian Universität München. He is Reader in Relativity Theory at Loughborough University. He has specialized in exact solutions in general relativity and other non-linear partial differential equations, and published a large number of papers, review articles and books.
Eduard Herlt, Friedrich-Schiller-Universität, Jena, Germany
Eduard Herlt is wissenschaftlicher Mitarbeiter at the Theoretisch Physikalisches Institut der Friedrich-Schiller-Universität Jena. Having studied physics as an undergraduate at Jena, he went on to complete his Ph.D. there as well as his Habilitation. He has had numerous publications including one previous book.