Flat and Curved Space-Times

Contents......Page 7
Introduction ......Page 9
1.1 The concept of a space-time ......Page 13
1.2 Causality and the speed of light ......Page 20
1.3 Relative motion in special relativity ......Page 32
2.1 Time ......Page 43
2.2 Distance ......Page 45
2.3 Simultaneity ......Page 49
2.4 World maps, world pictures, and radar maps ......Page 52
3.1 The Doppler effect ......Page 57
3.2 Relative velocity ......Page 67
3.3 Simultaneity ......Page 78
3.4 Time dilation ......Page 84
3.5 Length contraction ......Page 96
3.6 The whole package of kinematic effects ......Page 104
3.7 Relativistic dynamics ......Page 110
3.8 The consistency of physics ......Page 128
4.1 The Lorentz transformation ......Page 130
4.2 Space-time separation invariants ......Page 147
4.3 Some flat-space universes ......Page 170
5.1 The general concept ......Page 194
5.2 Acceleration and gravitation: the principle of equivalence ......Page 197
5.3 Freely falling motion and the meaning of geodesics ......Page 203
5.4 The metric form and the metric tensor ......Page 209
5.5 The field equations ......Page 214
5.6 Light rays ......Page 217
5.7 Causality ......Page 225
5.8 Parallel propagation along a curve ......Page 227
5.9 Further tests of Einstein's theory ......Page 230
5.10 Gravitational waves ......Page 234
5.11 Detection of gravitational waves ......Page 237
5.12 Alternative theories and approaches ......Page 240
6.1 The Schwarzschild solution ......Page 248
6.2 Spherical collapse to black holes ......Page 257
6.3 More general black holes ......Page 263
6.4 Black hole evaporation and thermodynamics ......Page 265
6.5 Black hole candidates and ways of detecting them ......Page 268
7.1 Space-time geometry ......Page 272
7.2 The evolution of the universe ......Page 279
7.3 Observable quantities ......Page 285
7.4 New observational data ......Page 292
7.5 The light cone, observational limits, and horizons ......Page 301
7.6 Steady-state and inflationary universes ......Page 309
7.7 Small universes ......Page 313
7.8 Alternative universes ......Page 316
7.9 Observational tests ......Page 319
8. Finale ......Page 321
Afterword ......Page 323
Appendices......Page 0
A. Line integrals ......Page 326
B. Four-vectors and relativistic dynamics ......Page 333
C. Four-vectors, electromagnetism, and energy-momentum conservation ......Page 349
Symbols used ......Page 376
Index ......Page 377