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Preface to the second edition | p. xi |
Preface to the first edition | p. xiii |
Special relativity | p. 1 |
Fundamental principles of special relativity (SR) theory | p. 1 |
Definition of an inertial observer in SR | p. 3 |
New units | p. 4 |
Spacetime diagrams | p. 5 |
Construction of the coordinates used by another observer | p. 6 |
Invariance of the interval | p. 9 |
Invariant hyperbolae | p. 14 |
Particularly important results | p. 17 |
The Lorentz transformation | p. 21 |
The velocity-composition law | p. 22 |
Paradoxes and physical intuition | p. 23 |
Further reading | p. 24 |
Appendix: The twin 'paradox' dissected | p. 25 |
Exercises | p. 28 |
Vector analysis in special relativity | p. 33 |
Definition of a vector | p. 33 |
Vector algebra | p. 36 |
The four-velocity | p. 41 |
The four-momentum | p. 42 |
Scalar product | p. 44 |
Applications | p. 46 |
Photons | p. 49 |
Further reading | p. 50 |
Exercises | p. 50 |
Tensor analysis in special relativity | p. 56 |
The metric tensor | p. 56 |
Definition of tensors | p. 56 |
The (01) tensors: one-forms | p. 58 |
The (02) tensors | p. 66 |
Metric as a mapping of vectors into one-forms | p. 68 |
Finally: (MN) tensors | p. 72 |
Index 'raising' and 'lowering' | p. 74 |
Differentiation of tensors | p. 76 |
Further reading | p. 77 |
Exercises | p. 77 |
Perfect fluids in special relativity | p. 84 |
Fluids | p. 84 |
Dust: the number-flux vector N | p. 85 |
One-forms and surfaces | p. 88 |
Dust again: the stress-energy tensor | p. 91 |
General fluids | p. 93 |
Perfect fluids | p. 100 |
Importance for general relativity | p. 104 |
Gauss' law | p. 105 |
Further reading | p. 106 |
Exercises | p. 107 |
Preface to curvature | p. 111 |
On the relation of gravitation to curvature | p. 111 |
Tensor algebra in polar coordinates | p. 118 |
Tensor calculus in polar coordinates | p. 125 |
Christoffel symbols and the metric | p. 131 |
Noncoordinate bases | p. 135 |
Looking ahead | p. 138 |
Further reading | p. 139 |
Exercises | p. 139 |
Curved manifolds | p. 142 |
Differentiable manifolds and tensors | p. 142 |
Riemannian manifolds | p. 144 |
Covariant differentiation | p. 150 |
Parallel-transport, geodesics, and curvature | p. 153 |
The curvature tensor | p. 157 |
Bianchi identities: Ricci and Einstein tensors | p. 163 |
Curvature in perspective | p. 165 |
Further reading | p. 166 |
Exercises | p. 166 |
Physics in a curved spacetime | p. 171 |
The transition from differential geometry to gravity | p. 171 |
Physics in slightly curved spacetimes | p. 175 |
Curved intuition | p. 177 |
Conserved quantities | p. 178 |
Further reading | p. 181 |
Exercises | p. 181 |
The Einstein field equations | p. 184 |
Purpose and justification of the field equations | p. 184 |
Einstein's equations | p. 187 |
Einstein's equations for weak gravitational fields | p. 189 |
Newtonian gravitational fields | p. 194 |
Further reading | p. 197 |
Exercises | p. 198 |
Gravitational radiation | p. 203 |
The propagation of gravitational waves | p. 203 |
The detection of gravitational waves | p. 213 |
The generation of gravitational waves | p. 227 |
The energy carried away by gravitational waves | p. 234 |
Astrophysical sources of gravitational waves | p. 242 |
Further reading | p. 247 |
Exercises | p. 248 |
Spherical solutions for stars | p. 256 |
Coordinates for spherically symmetric spacetimes | p. 256 |
Static spherically symmetric spacetimes | p. 258 |
Static perfect fluid Einstein equations | p. 260 |
The exterior geometry | p. 262 |
The interior structure of the star | p. 263 |
Exact interior solutions | p. 266 |
Realistic stars and gravitational collapse | p. 269 |
Further reading | p. 276 |
Exercises | p. 277 |
Schwarzschild geometry and black holes | p. 281 |
Trajectories in the Schwarzschild spacetime | p. 281 |
Nature of the surface r = 2M | p. 298 |
General black holes | p. 304 |
Real black holes in astronomy | p. 318 |
Quantum mechanical emission of radiation by black holes: the Hawking process | p. 323 |
Further reading | p. 327 |
Exercises | p. 328 |
Cosmology | p. 335 |
What is cosmology? | p. 335 |
Cosmological kinematics: observing the expanding universe | p. 337 |
Cosmological dynamics: understanding the expanding universe | p. 353 |
Physical cosmology: the evolution of the universe we observe | p. 361 |
Further reading | p. 369 |
Exercises | p. 370 |
Summary of linear algebra | p. 374 |
References | p. 378 |
Index | p. 386 |
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