Exact Solutions of Einstein's Field Equations
Cambridge Univ Pr, 1/1/2009
EAN 9780521467025, ISBN10: 0521467020
Paperback, 24.4 x 17.5 x 4.3 cm
Language: English
A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.
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=ÃÆ’=0=R11=R14=R44, ÃŽËœ+iÉ≠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.
'... not only is the book an unrivalled source of knowledge on what has been charted of the rugged landscape of curved space-times, but, additionally, it is a well-organized and concise reference in matters of differential geometry.' General Relativity and Gravitation