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| Preface to the second edition | |
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| Preface to the first edition | |
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| Special relativity | |
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| Fundamental principles of special relativity (SR) theory | |
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| Definition of an inertial observer in SR | |
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| New units | |
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| Spacetime diagrams | |
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| Construction of the coordinates used by another observer | |
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| Invariance of the interval | |
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| Invariant hyperbolae | |
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| Particularly important results | |
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| The Lorentz transformation | |
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| The velocity-composition law | |
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| Paradoxes and physical intuition | |
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| Further reading | |
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| Appendix: The twin 'paradox' dissected | |
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| Exercises | |
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| Vector analysis in special relativity | |
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| Definition of a vector | |
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| Vector algebra | |
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| The four-velocity | |
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| The four-momentum | |
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| Scalar product | |
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| Applications | |
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| Photons | |
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| Further reading | |
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| Exercises | |
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| Tensor analysis in special relativity | |
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| The metric tensor | |
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| Definition of tensors | |
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| The (01) tensors: one-forms | |
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| The (02) tensors | |
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| Metric as a mapping of vectors into one-forms | |
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| Finally: (MN) tensors | |
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| Index 'raising' and 'lowering' | |
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| Differentiation of tensors | |
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| Further reading | |
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| Exercises | |
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| Perfect fluids in special relativity | |
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| Fluids | |
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| Dust: the number-flux vector N | |
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| One-forms and surfaces | |
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| Dust again: the stress-energy tensor | |
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| General fluids | |
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| Perfect fluids | |
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| Importance for general relativity | |
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| Gauss' law | |
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| Further reading | |
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| Exercises | |
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| Preface to curvature | |
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| On the relation of gravitation to curvature | |
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| Tensor algebra in polar coordinates | |
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| Tensor calculus in polar coordinates | |
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| Christoffel symbols and the metric | |
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| Noncoordinate bases | |
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| Looking ahead | |
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| Further reading | |
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| Exercises | |
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| Curved manifolds | |
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| Differentiable manifolds and tensors | |
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| Riemannian manifolds | |
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| Covariant differentiation | |
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| Parallel-transport, geodesics, and curvature | |
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| The curvature tensor | |
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| Bianchi identities: Ricci and Einstein tensors | |
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| Curvature in perspective | |
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| Further reading | |
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| Exercises | |
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| Physics in a curved spacetime | |
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| The transition from differential geometry to gravity | |
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| Physics in slightly curved spacetimes | |
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| Curved intuition | |
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| Conserved quantities | |
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| Further reading | |
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| Exercises | |
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| The Einstein field equations | |
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| Purpose and justification of the field equations | |
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| Einstein's equations | |
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| Einstein's equations for weak gravitational fields | |
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| Newtonian gravitational fields | |
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| Further reading | |
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| Exercises | |
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| Gravitational radiation | |
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| The propagation of gravitational waves | |
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| The detection of gravitational waves | |
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| The generation of gravitational waves | |
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| The energy carried away by gravitational waves | |
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| Astrophysical sources of gravitational waves | |
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| Further reading | |
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| Exercises | |
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| Spherical solutions for stars | |
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| Coordinates for spherically symmetric spacetimes | |
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| Static spherically symmetric spacetimes | |
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| Static perfect fluid Einstein equations | |
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| The exterior geometry | |
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| The interior structure of the star | |
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| Exact interior solutions | |
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| Realistic stars and gravitational collapse | |
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| Further reading | |
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| Exercises | |
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| Schwarzschild geometry and black holes | |
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| Trajectories in the Schwarzschild spacetime | |
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| Nature of the surface r = 2M | |
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| General black holes | |
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| Real black holes in astronomy | |
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| Quantum mechanical emission of radiation by black holes: the Hawking process | |
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| Further reading | |
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| Exercises | |
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| Cosmology | |
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| What is cosmology? | |
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| Cosmological kinematics: observing the expanding universe | |
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| Cosmological dynamics: understanding the expanding universe | |
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| Physical cosmology: the evolution of the universe we observe | |
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| Further reading | |
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| Exercises | |
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| Summary of linear algebra | |
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| References | |
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| Index | |