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Einstein spaces /
Einstein Spaces presents the mathematical basis of the theory of gravitation and discusses the various spaces that form the basis of the theory of relativity. This book examines the contemporary development of the theory of relativity, leading to the study of such problems as gravitational radiation...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1969]
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| Edición: | [1st English ed.]. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Einstein Spaces; Copyright Page; Table of Contents; Preface to the English Edition; Foreword; Notation; Chapter 1. Basic Tensor Analysis; 1. Riemann Manifolds; 2. Tensor Algebra; 3. Covariant Differentiation; 4. Parallel Displacement in a Vn Space; 5. Curvature Tensor of a Vn Space; 6. Geodesies; 7. Special Systems of Coordinates in Vn; 8. Riemannian Curvature of Vn. Spaces of Constant Curvature; 9. The Principal Axes Theorem for a Tensor; 10. Lie Groups in Vn; Chapter 2. Einstein Spaces; 11. The Basis of the Special Theory of Relativity. Lorentz Transformations.
- 12. Field Equations in the Relativistic Theory of Gravitation13. Einstein Spaces; 14. Some Solutions of the Gravitational Field Equations; Chapter 3. General Classification of Gravitational Fields; 15. Bivector Spaces; 16. Classification of Einstein Spaces; 17. Principal Curvatures; 18. The Classification of Einstein Spaces for n = 4; 19. The Canonical Form of the Matrix (Rab) for Ti and �Ti Spaces; 20. Classification of General Gravitational Fields; 21. Complex Representation of Minkowski Space Tensors; 22. Basis of the Complete System of Second Order Invariants of a V4 Space.
- Chapter 4. Motions in Empty Space23. Classification of Ti by Groups of Motions; 24. Non-isomorphic Structures of Groups of Motions Admitted by Empty Spaces; 25. Spaces of Maximum Mobility T1, T2 and T3; 26. T1 Spaces Admitting Motions; 27. T2 and T3 Spaces Admitting Motions; 28. Summary of Results. Survey of Well-known Solutions of the Field Equations; Chapter 5. Classification of General Gravitational Fields by Groups of Motions; 29. Gravitational Fields Admitting a Gr Group (r d"2); 30. Gravitational Fields Admitting a G3 Group of Motions Acting on a V2 or V2.
- 31. Gravitational Fields Admitting a G3 Group of Motions Acting on a V3 or V332. Gravitational Fields Admitting a Simply-transitive or Intransitive G4 Group of Motions; 33. Gravitational Fields Admitting Groups of Motions Gr (r d"5); Chapter 6. Conformal Mapping of Einstein Spaces; 34. Conformal Mapping of Riemann Spaces; 35. Conformal Mapping of Riemann Spaces on Einstein Spaces; 36. Conformal Mapping of Einstein Spaces on Einstein Spaces ; Non-isotropic Case; 37. Conformal Mapping of Einstein Spaces ; Isotropie Case; Chapter 7. Geodesic Mapping of Gravitational Fields.
- 38. Historical Survey39. Algebraic Classification of the Possible Cases; 40. The Invariant Equations for gii in a Non-holonomic Orthonormal Tetrad; 41. The Canonical Forms of the Metrics of V4 and V4 in a Holonomic Coordinate System; 42. The Projective Mapping of Einstein Spaces; Chapter 8. The Cauchy Problem for the Einstein Field Equations; 43. The Einstein Field Equations; 44. The Exterior Cauchy Problem; 45. Freedom Available in Choosing Field Potentials for an Einstein Space; 46. Characteristic and Bicharacteristic Manifolds; 47. The Energy-momentum Tensor.