Relativistic cosmology has in recent years become one of the most exciting and active branches of current research. In conference after conference the view is expressed that cosmology today is where particle physics was forty years ago, with major discoveries just waiting to happen. Also gravitational wave detectors, presently under construction or in the testing phase, promise to open up an entirely novel field of physics. It is to take into account such recent developments, as well as to improve the basic text, that this second edition has been undertaken. The most affected is the last part on cosmology, but there are smaller additions, corrections, and additional exercises throughout. The books basic purpose is to make relativity come alive conceptually. Hence the emphasis on the foundations and the logical subtleties rather than on the mathematics or the detailed experiments per se. Aided by some 300 exercises, the book promotes a deep understanding and the confidence to tackle any fundamental relativistic problem.
Author(s): Wolfgang Rindler
Edition: 2
Year: 2006
Language: English
Pages: 448
Contents......Page 12
Introduction......Page 18
1.1 Definition of relativity......Page 20
1.2 Newton’s laws and inertial frames......Page 21
1.3 The Galilean transformation......Page 22
1.4 Newtonian relativity......Page 23
1.5 Objections to absolute space; Mach’s principle......Page 24
1.7 Michelson and Morley’s search for the ether......Page 26
1.8 Lorentz’s ether theory......Page 27
1.9 Origins of special relativity......Page 29
1.10 Further arguments for Einstein’s two postulates......Page 31
1.11 Cosmology and first doubts about inertial frames......Page 32
1.12 Inertial and gravitational mass......Page 33
1.13 Einstein’s equivalence principle......Page 35
1.14 Preview of general relativity......Page 37
1.15 Caveats on the equivalence principle......Page 39
1.16 Gravitational frequency shift and light bending......Page 41
Exercises 1......Page 44
I: Special Relativity......Page 48
2.1 On the nature of physical theories......Page 50
2.2 Basic features of special relativity......Page 51
2.3 Relativistic problem solving......Page 53
2.4 Relativity of simultaneity, time dilation and length contraction: a preview......Page 55
2.5 The relativity principle and the homogeneity and isotropy of inertial frames......Page 56
2.6 The coordinate lattice; Definitions of simultaneity......Page 58
2.7 Derivation of the Lorentz transformation......Page 60
2.8 Properties of the Lorentz transformation......Page 64
2.9 Graphical representation of the Lorentz transformation......Page 66
2.10 The relativistic speed limit......Page 71
2.11 Which transformations are allowed by the relativity principle?......Page 74
Exercises 2......Page 75
3.2 World-picture and world-map......Page 78
3.3 Length contraction......Page 79
3.4 Length contraction paradox......Page 80
3.5 Time dilation; The twin paradox......Page 81
3.6 Velocity transformation; Relative and mutual velocity......Page 85
3.7 Acceleration transformation; Hyperbolic motion......Page 87
3.8 Rigid motion and the uniformly accelerated rod......Page 88
Exercises 3......Page 90
4.2 The drag effect......Page 94
4.3 The Doppler effect......Page 95
4.4 Aberration......Page 98
4.5 The visual appearance of moving objects......Page 99
Exercises 4......Page 102
5.1 The discovery of Minkowski space......Page 106
5.2 Three-dimensional Minkowski diagrams......Page 107
5.3 Light cones and intervals......Page 108
5.4 Three-vectors......Page 111
5.5 Four-vectors......Page 114
5.6 The geometry of four-vectors......Page 118
5.7 Plane waves......Page 120
Exercises 5......Page 122
6.1 Domain of sufficient validity of Newtonian mechanics......Page 125
6.2 The axioms of the new mechanics......Page 126
6.3 The equivalence of mass and energy......Page 128
6.4 Four-momentum identities......Page 131
6.5 Relativistic billiards......Page 132
6.6 The zero-momentum frame......Page 134
6.7 Threshold energies......Page 135
6.8 Light quanta and de Broglie waves......Page 136
6.9 The Compton effect......Page 138
6.10 Four-force and three-force......Page 140
Exercises 6......Page 143
7.1 Tensors: Preliminary ideas and notations......Page 147
7.2 Tensors: Definition and properties......Page 149
7.3 Maxwell’s equations in tensor form......Page 156
7.4 The four-potential......Page 160
7.5 Transformation of e and b; The dual field......Page 163
7.6 The field of a uniformly moving point charge......Page 165
7.7 The field of an infinite straight current......Page 167
7.8 The energy tensor of the electromagnetic field......Page 168
7.9 From the mechanics of the field to the mechanics of material continua......Page 171
Exercises 7......Page 174
II: General Relativity......Page 180
8.1 Curved surfaces......Page 182
8.2 Curved spaces of higher dimensions......Page 186
8.3 Riemannian spaces......Page 189
8.4 A plan for general relativity......Page 194
Exercises 8......Page 197
9.1 The coordinate lattice......Page 200
9.2 Synchronization of clocks......Page 201
9.3 First standard form of the metric......Page 203
9.4 Newtonian support for the geodesic law of motion......Page 205
9.5 Symmetries and the geometric characterization of static and stationary spacetimes......Page 208
9.6 Canonical metric and relativistic potentials......Page 212
9.7 The uniformly rotating lattice in Minkowski space......Page 215
Exercises 9......Page 217
10.1 Tensors for general relativity......Page 220
10.2 Geodesics......Page 221
10.3 Geodesic coordinates......Page 225
10.4 Covariant and absolute differentiation......Page 227
10.5 The Riemann curvature tensor......Page 234
10.6 Einstein’s vacuum field equations......Page 238
Exercises 10......Page 241
11.1 Derivation of the metric......Page 245
11.2 Properties of the metric......Page 247
11.3 The geometry of the Schwarzschild lattice......Page 248
11.4 Contributions of the spatial curvature to post-Newtonian effects......Page 250
11.5 Coordinates and measurements......Page 252
11.6 The gravitational frequency shift......Page 253
11.7 Isotropic metric and Shapiro time delay......Page 254
11.8 Particle orbits in Schwarzschild space......Page 255
11.9 The precession of Mercury’s orbit......Page 258
11.10 Photon orbits......Page 262
11.11 Deflection of light by a spherical mass......Page 265
11.12 Gravitational lenses......Page 267
11.13 de Sitter precession via rotating coordinates......Page 269
Exercises 11......Page 271
12.1 Schwarzschild black holes......Page 275
12.2 Potential energy; A general-relativistic ‘proof’ of E = mc[sup(2)]......Page 280
12.3 The extendibility of Schwarzschild spacetime......Page 282
12.4 The uniformly accelerated lattice......Page 284
12.5 Kruskal space......Page 289
12.6 Black-hole thermodynamics and related topics......Page 296
Exercises 12......Page 298
13.2 The plane-wave metric......Page 301
13.3 When wave meets dust......Page 304
13.4 Inertial coordinates behind the wave......Page 305
13.5 When wave meets light......Page 307
13.6 The Penrose topology......Page 308
13.7 Solving the field equation......Page 310
Exercises 13......Page 312
14.1 The laws of physics in curved spacetime......Page 313
14.2 At last, the full field equations......Page 316
14.3 The cosmological constant......Page 320
14.4 Modified Schwarzschild space......Page 321
14.5 de Sitter space......Page 323
14.6 Anti-de Sitter space......Page 329
Exercises 14......Page 331
15.1 The basic equations......Page 335
15.2 Gravitational waves; The TT gauge......Page 340
15.3 Some physics of plane waves......Page 342
15.4 Generation and detection of gravitational waves......Page 347
15.5 The electromagnetic analogy in linearized GR......Page 352
Exercises 15......Page 358
III: Cosmology......Page 362
16.1 The basic facts......Page 364
16.2 Beginning to construct the model......Page 375
16.3 Milne’s model......Page 377
16.4 The Friedman–Robertson–Walker metric......Page 380
16.5 Robertson and Walker’s theorem......Page 385
Exercises 16......Page 386
17.1 Representation of FRW universes by subuniverses......Page 390
17.2 The cosmological frequency shift......Page 391
17.3 Cosmological horizons......Page 393
17.4 The apparent horizon......Page 399
17.5 Observables......Page 401
Exercises 17......Page 405
18.1 Applying the field equations......Page 408
18.2 What the field equations tell us......Page 410
18.3 The Friedman models......Page 414
18.4 Once again, comparison with observation......Page 423
18.5 Inflation......Page 428
18.6 The anthropic principle......Page 432
Exercises 18......Page 433
Appendix: Curvature tensor components for the diagonal metric......Page 436
C......Page 440
E......Page 441
G......Page 442
I......Page 443
M......Page 444
R......Page 445
S......Page 446
Z......Page 447
