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 spacetime 
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. Repeatedindex 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. Energymomentum tensor 
22. Energymomentum tensor for a fluid 
23. Angular momentum 

Exercises 3 
Chapter 4 Special Relativity Electrodynamics 
24. 4Current density 
25. 4Vector potential 
26. The field tensor 
27. Lorentz transformations of electric and magnetic vectors 
28. The Lorentz force 
29. The engerymomentum tensor for an electromagnetic field 

Exercises 4 
Chapter 5 General Tensor Calculus. Riemannian Space 
30. Generalized Ndimensional 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 RiemannChristoffel 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 RobertsonWalker 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 