Exact Solutions of Einstein's Field Equations: (Cambridge Monographs on Mathematical Physics)

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.

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.

About the Author :
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 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 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 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 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.

Review :
'… 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 '… 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