Preface |
List of Constants |
Chapter 1 Special Principle of Relativity. Lorentz Transformations |
1. Newton's laws of motion |
2. Covariance of the laws of motion |
3. Special principle of relativity |
4. Lorentz transformations. Minkowski space-time |
5. The special Lorentz transformation |
6. Fitzgerald contraction. Time dilation |
7. Spacelike and timelike intervals. Light cone |
|
Exercises 1 |
Chapter 2 Orthogonal Transformations. Cartesian Tensors |
8. Orthogonal transformations |
9. Repeated-index summation convention |
10. Rectangular Cartesian tensors |
11. Invariants. Gradients. Derivatives of tensors |
12. Contraction. Scalar product. Divergence |
13. Pseudotensors |
14. Vector products. Curl |
|
Exercises 2 |
Chapter 3 Special Relativity Mechanics |
15. The velocity vector |
16. Mass and momentum |
17. The force vector. Energy |
18. Lorentz transformation equations for force |
19. Fundamental particles. Photon and neutrino |
20. Lagrange's and Hamilton's equations |
21. Energy-momentum tensor |
22. Energy-momentum tensor for a fluid |
23. Angular momentum |
|
Exercises 3 |
Chapter 4 Special Relativity Electrodynamics |
24. 4-Current density |
25. 4-Vector potential |
26. The field tensor |
27. Lorentz transformations of electric and magnetic vectors |
28. The Lorentz force |
29. The engery-momentum tensor for an electromagnetic field |
|
Exercises 4 |
Chapter 5 General Tensor Calculus. Riemannian Space |
30. Generalized N-dimensional spaces |
31. Contravariant and covariant tensors |
32. The quotient theorem. Conjugate tensors |
33. Covariant derivatives. Parallel displacement. Affine connection |
34. Transformation of an affinity |
35. Covariant derivatives of tensors |
36. The Riemann-Christoffel curvature tensor |
37. Metrical connection. Raising and lowering indices |
38. Scalar products. Magnitudes of vectors |
39. Geodesic frame. Christoffel symbols |
40. Bianchi identity |
41. The covariant curvature tensor |
42. Divergence. The Laplacian. Einstein's tensor |
43. Geodesics |
|
Exercises 5 |
Chapter 6 General Theory of Relativity |
44. Principle of equivalence |
45. Metric in a gravitational field |
46. Motion of a free particle in a gravitational field |
47. Einstein's law of gravitation |
48. Acceleration of a particle in a weak gravitational field |
49. Newton's law of gravit |
50. Freely falling dust cloud |
51. Metrics with spherical symmetry |
52. Schwarzchild's solution |
53. Planetary orbits |
54. Gravitational deflection of a light ray |
55. Gravitational displacement of spectral lines |
56. Maxwell's equations in a gravitational field |
57. Black holes |
58. Gravitational waves |
|
Exercises 6 |
Chapter 7 Cosmology |
59. Cosmological principle. Cosmical time |
60. Spaces of constant curvature |
61. The Robertson-Walker metric |
62. Hubble's constant and the deceleration parameter |
63. Red shifts of galaxies |
64. Luminosity distance |
65. Cosmic dynamics |
66. Model universes of Einstein and de Sitter |
67. Friedmann universes |
68. Radiation model |
69. Particle and event horizons |
Exercises 7 |
References |
Bibliography |
Index |