Guidelines for the reader Chapter 0 Preliminaries 0.0 Review and notation 0.1 Physics background 0.2 Preview of relativity Chapter 1 Spacetimes 1.0 Review and notation 1.1 Causal character 1.2 Time orientability 1.3 Spacetimes 1.4 Examples of spacetimes Chapter 2 Observers 2.0 Mathematical preliminaries 2.1 Observers and instantaneous observers 2.2 Gyroscope axes 2.3 Reference frames Chapter 3 Electromagnetism and matter PART ONE: BASIC CONCEPTS 3.0 Review and notation 3.1 Particles 3.2 Particle flows 3.3 Stress-energy tensors 3.4 Electromagnetism 3.5 Matter and relativistic models PART TWO: INTERACTIONS 3.6 Some mathematical methods 3.7 Maxwell's equations 3.8 Particle dynamics 3.9 Matter equations: an example 3.10 Energy-momentum 『conservation' 3.11 Two initial value theorems 3.12 Appropriate matter equations PART THREE: OTHER MATTER MODELS 3.13 Exampies 3.14 Normal stress-energy tensors 3.15 Perfect fluids Chapter 4 The Einstein field equation 4.0 Review and notation 4.1 The Einstein field equation 4.2 Ricci flat spacetimes 4.3 Gravitational attraction and the phenomenon of collapse Chapter 5 Photons 5.0 Mathematical preliminaries 5.1 Photons 5.2 Light signals 5.3 Synchronizable reference frames 5.4 Frequency ratio 5.5 Photon distribution functions 5.6 Integration on lightcones 5.7 A photon gas
Chapter 6 Cosmology 6.0 Review, notation and mathematical preliminaries 6.1 Data 6.2 Cosmological models 6.3 The Einstein-de Sitter model 6.4 Simple cosmological models 6.5 The early universe 6.6 Other models 6.7 Appendix: Luminosity distance in the Einstein-de Sitter model Chapter 7 Further applications 7.0 Review and notation 7.1 Preview 7.2 Stationary spacetimes 7.3 The geometry of Schwarzschild spacetimes 7.4 The solar system 7.5 Black holes 7.6 Gravitational plane waves Chapter 8 Optional exercises:relativity 8.1 Lorentzian algebra 8.2 Differential topology and geometry 8.3 Chronology and causality 8.4 Isometries and characterizations of gravitational fields 8.5 The Einstein field equation 8.6 Gases Chapter 9 Optional exercises: Newtonian analogues 9.0 Review and notation 9.1 Maxwell's equations 9.2 Particles 9.3 Gravity Glossary of symbols Bibliography Index of basic notations Index
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