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Exact Solutions of Einstein's Field Equations

Author: Hans Stephani; D Kramer; Malcolm MacCallum; Cornelius Hoenselaers; Eduard Herlt
Publisher: Cambridge : Cambridge University Press, 2003.
Series: Cambridge monographs on mathematical physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Hans Stephani; D Kramer; Malcolm MacCallum; Cornelius Hoenselaers; Eduard Herlt
ISBN: 9780511535185 051153518X 9780521461368 0521461367
OCLC Number: 776966361
Notes: Title from publishers bibliographic system (viewed on 22 Dec 2011).
Description: 1 online resource (732 pages)
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 = =0=R11=R14=R44, +i 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.
Series Title: Cambridge monographs on mathematical physics.
Responsibility: Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers, Eduard Herlt.

Abstract:

A paperback edition of a classic text, this book contains six new chapters, covering generation methods and their application, colliding waves, classification of metrics by invariants and treatments  Read more...

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'... 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 Read more...

 
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