Exact Solutions of Einstein's Field Equations
2nd Edition
Part of Cambridge Monographs on Mathematical Physics
 Authors:
 Hans Stephani, FriedrichSchillerUniversität, Jena, Germany
 Dietrich Kramer, FriedrichSchillerUniversität, Jena, Germany
 Malcolm MacCallum, Queen Mary University of London
 Cornelius Hoenselaers, Loughborough University
 Eduard Herlt, FriedrichSchillerUniversität, Jena, Germany
 Date Published: September 2009
 availability: Available
 format: Paperback
 isbn: 9780521467025
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A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, EinsteinMaxwell, 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.
Read more 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, EinsteinMaxwell, pure radiation and perfect fluid sources
Reviews & endorsements
'… not only is the book an unrivalled source of knowledge on what has been charted of the rugged landscape of curved spacetimes, but, additionally, it is a wellorganized and concise reference in matters of differential geometry.' General Relativity and Gravitation
See more reviews'… a remarkable work, and indispensable to any serious practitioner of classical general relativity.' Mathematics Today
'… will be a lighthouse for those navigating in the ever expanding ocean of exact solutions to Einstein's equations.' Zentralblatt MATH
'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.' Mathematical Reviews
'We should be thankful to the authors for having undertaken this project. The second edition, like the first one, is a real masterpiece.' CERN Courier
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×Product details
 Edition: 2nd Edition
 Date Published: September 2009
 format: Paperback
 isbn: 9780521467025
 length: 732 pages
 dimensions: 244 x 175 x 43 mm
 weight: 1.2kg
 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 energymovement 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 spacetimes
13. Hypersurfacehomogeneous spacetimes
14. Spatiallyhomogeneous perfect fluid cosmologies
15. Groups G3 on nonnull orbits V2. Spherical and plane symmetry
16. Sphericallysymmetric perfect fluid solutions
17. Groups G2 and G1 on nonnull orbits
18. Stationary gravitational fields
19. Stationary axisymmetric fields: basic concepts and field equations
20. Stationary axisymmetiric vacuum solutions
21. Nonempty 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. Nondiverging 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 fourdimensional Riemannian manifolds
Part V. Tables:
38. The interconnections between the main classification schemes
References
Index.
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