EXCERPTS FROM THE PREFACES TO THE FIRST AND SECOND EDITIONS	ix
PREFACE TO THE FOURTH ENGLISH EDITION	x
EDITOR’S PREFACE TO THE SEVENTH RUSSIAN EDITION	xi
NOTATION	xiii
CHAPTER 1. THE PRINCIPLE OF RELATIVITY	1
1 Velocity of propagation of interaction	1
2 Intervals	3
3 Proper time	7
4 The Lorentz transformation	9
5 Transformation of velocities	12
6 Four-vectors	14
7 Four-dimensional velocity	23
CHAPTER 2. RELATIVISTIC MECHANICS	25
8 The principle of least action	25
9 Energy and momentum	26
10 Transformation of distribution functions	30
11 Decay of particles	32
12 Invariant cross-section	36
13 Elastic collisions of particles	38
14 Angular momentum	42
CHAPTER 3. CHARGES IN ELECTROMAGNETIC FIELDS	46
15 Elementary particles in the theory of relativity	46
16 Four-potential of a field	47
17 Equations of motion of a charge in a field	49
18 Gauge invariance	52
19 Constant electromagnetic field	53
20 Motion in a constant uniform electric field	55
21 Motion in a constant uniform magnetic field	56
22 Motion of a charge in constant uniform electric and magnetic fields	59
23 The electromagnetic field tensor	64
24 Lorentz transformation of the field	66
25 Invariants of the field	67

CHAPTER 4. THE ELECTROMAGNETIC FIELD EQUATIONS	70
26 The first pair of Maxwell’s equations	70
27 The action function of the electromagnetic field	71
28 The four-dimensional current vector	73
29 The equation of continuity	76
30 The second pair of Maxwell equations	78
31 Energy density and energy flux	80
32 The energy-momentum tensor	82
33 Energy-momentum tensor of the electromagnetic field	86
34 The virial theorem	90
35 The energy-momentum tensor for macroscopic bodies	92
CHAPTER 5. CONSTANT ELECTROMAGNETIC FIELDS	95
36 Coulomb’s law	95
37 Electrostatic energy of charges	96
38 The field of a uniformly moving charge	98
39 Motion in the Coulomb field	100
40 The dipole moment	103
41 Multipole moments	105
42 System of charges in an external field	108
43 Constant magnetic field	110
44 Magnetic moments	111
45 Larmor’s theorem	113
CHAPTER 6. ELECTROMAGNETIC WAVES	116
46 The wave equation	116
47 Plane waves	118
48 Monochromatic plane waves	123
49 Spectral resolution	128
50 Partially polarized light	129
51 The Fourier resolution of the electrostatic field	134
52 Characteristic vibrations of the field	135
CHAPTER 7. THE PROPAGATION OF LIGHT	140
53 Geometrical optics	140
54 Intensity	143
55 The angular eikonal	145
56 Narrow bundles of rays	147
57 Image formation with broad bundles of rays	153
58 The limits of geometrical optics	154
59 Diffraction	156
60 Fresnel diffraction	162
61 Fraunhofer diffraction	165

CONTENTS	vii
CHAPTER 8. THE FIELD OF MOVING CHARGES	171
62 The retarded potentials	171
63 The Lienard–Wiechert potentials	173
64 Spectral resolution of the retarded potentials	176
65 The Lagrangian to terms of second order	179
CHAPTER 9. RADIATION OF ELECTROMAGNETIC WAVES	184
66 The field of a system of charges at large distances	184
67 Dipole radiation	187
68 Dipole radiation during collisions	191
69 Radiation of low frequency in collisions	193
70 Radiation in the case of Coulomb interaction	195
71 Quadrupole and magnetic dipole radiation	203
72 The field of the radiation at near distances	206
73 Radiation from a rapidly moving charge	210
74 Synchrotron radiation (magnetic bremsstrahlung)	215
75 Radiation damping	222
76 Radiation damping in the relativistic case	226
77 Spectral resolution of the radiation in the ultrarelativistic case	230
78 Scattering by free charges	233
79 Scattering of low-frequency waves	238
80 Scattering of high-frequency waves	240
CHAPTER 10. PARTICLE IN A GRAVITATIONAL FIELD	243
81 Gravitational fields in nonrelativistic mechanics	243
82 The gravitational field in relativistic mechanics	244
83 Curvilinear coordinates	247
84 Distances and time intervals	251
85 Covariant differentiation	255
86 The relation of the Christoffel symbols to the metric tensor	260
87 Motion of a particle in a gravitational field	263
88 The constant gravitational field	266
89 Rotation	273
90 The equations of electrodynamics in the presence of a gravitational field	275
CHAPTER 11. THE GRAVITATIONAL FIELD EQUATIONS	278
91 The curvature tensor	278
92 Properties of the curvature tensor	281
93 The action function for the gravitational field	287
94 The energy-momentum tensor	290
95 The Einstein equations	295
96 The energy-momentum pseudotensor of the gravitational field	301
97 The synchronous reference system	307
98 The tetrad representation of the Einstein equations	313

CHAPTER 12. THE FIELD OF GRAVITATING BODIES	316
99 Newton’s law	316
100 The centrally symmetric gravitational field	320
101 Motion in a centrally symmetric gravitational field	328
102 Gravitational collapse of a spherical body	331
103 Gravitational collapse of a dustlike sphere	338
104 Gravitational collapse of nonspherical and rotating bodies	344
105 Gravitational fields at large distances from bodies	353
106 The equations of motion of a system of bodies in the second approximation	360
CHAPTER 13. GRAVITATIONAL WAVES	368
107 Weak gravitational waves	368
108 Gravitational waves in curved space-time	370
109 Strong gravitational waves	373
110 Radiation of gravitational waves	376
CHAPTER 14. RELATIVISTIC COSMOLOGY	382
111 Isotropic space	382
112 The closed isotropic model	386
113 The open isotropic model	390
114 The red shift	394
115 Gravitational stability of an isotropic universe	400
116 Homogeneous spaces	406
117 The flat anisotropic model	412
118 Oscillating regime of approach to a singular point	416
119 The time singularity in the general cosmological solution of the Einstein equations	420
INDEX	425

Prefaces

Table of Contents