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 of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics.
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 of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics.
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.
Inhaltsangabe
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 =s=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.
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 =s=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.
Rezensionen
'... 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
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