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Introduction | 1 | |
1. | Space--time diagrams and the foundations of special relativity | 5 |
1.1 | The concept of a space--time | 5 |
1.2 | Causality and the speed of light | 12 |
1.3 | Relative motion in special relativity | 24 |
2. | Fundamentals of measurement | 35 |
2.1 | Time | 35 |
2.2 | Distance | 37 |
2.3 | Simultaneity | 41 |
2.4 | World maps, world pictures, and radar maps | 44 |
3. | Measurements in flat space--times | 49 |
3.1 | The Doppler effect | 49 |
3.2 | Relative velocity | 59 |
3.3 | Simultaneity | 70 |
3.4 | Time dilation | 76 |
3.5 | Length contraction | 88 |
3.6 | The whole package of kinematic effects | 96 |
3.7 | Relativistic dynamics | 102 |
3.8 | The consistency of physics | 120 |
4. | The Lorentz transformation and the invariant interval | 122 |
4.1 | The Lorentz transformation | 122 |
4.2 | Space--time separation invariants | 139 |
4.3 | Some flat-space universes | 162 |
5. | Curved space--times | 186 |
5.1 | The general concept | 186 |
5.2 | Acceleration and gravitation: the principle of equivalence | 189 |
5.3 | Freely falling motion and the meaning of geodesics | 195 |
5.4 | The metric form and the metric tensor | 201 |
5.5 | The field equations | 206 |
5.6 | Light rays | 209 |
5.7 | Causality | 217 |
5.8 | Parallel propagation along a curve | 219 |
5.9 | Further tests of Einstein's theory | 222 |
5.10 | Gravitational waves | 226 |
5.11 | Detection of gravitational waves | 229 |
5.12 | Alternative theories and approaches | 232 |
6. | Spherical and stellar collapse | 240 |
6.1 | The Schwarzschild solution | 240 |
6.2 | Spherical collapse to black holes | 249 |
6.3 | More general black holes | 255 |
6.4 | Black hole evaporation and thermodynamics | 257 |
6.5 | Black hole candidates and ways of detecting them | 260 |
7. | Simple cosmological models | 264 |
7.1 | Space--time geometry | 264 |
7.2 | The evolution of the universe | 271 |
7.3 | Observable quantities | 277 |
7.4 | New observational data | 284 |
7.5 | The light cone, observational limits, and horizons | 293 |
7.6 | Steady-state and inflationary universes | 301 |
7.7 | Small universes | 305 |
7.8 | Alternative universes | 308 |
7.9 | Observational tests | 311 |
8. | Finale | 313 |
Afterword | 315 | |
Appendices | ||
A. | Line integrals | 318 |
B. | Four-vectors and relativistic dynamics | 325 |
C. | Four-vectors, electromagnetism, and energy--momentum conservation | 341 |
Symbols used | 368 | |
Index | 369 |
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