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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