Table of Contents
Chapter 1 Introduction 1
Chapter 2 Essentials of Special Relativity 11
2.1 Basic principles 11
2.2 The spacetime interval and the Lorentz transformation 13
2.3 Lorentz contraction and time dilation 15
2.4 Causality 17
2.5 Transformation of velocity and the aberration of light 19
2.6 Four-vectors and four-tensors 21
2.7 Special relativistic dynamics 23
2.8 Relativistic Doppler shift 26
Chapter 3 Bondi's k-Calculus Approach to Special Relativity 31
3.1 Introduction 31
3.2 Velocity-Doppler factor connection 33
3.3 Composition law for velocities and Doppler factors 35
3.4 Derivation of the Lorentz transformation 38
3.5 The twin or clock paradox 40
Chapter 4 Essentials of General Relativity 47
4.1 The need for a new theory of gravity 47
4.2 The Principle of Equivalence 48
4.3 The metric tensor 49
4.4 Basic tensor calculus-introduction 50
4.5 Parallel transport, spacetime curvature and the Riemann tensor 54
4.6 Geodesics 56
4.7 Covariant conservation laws and the Einstein field equations 57
4.8 Einstein-Maxwell equations and motion of a charged body in general relativity 61
4.9 Summary of the steps from Newtonian gravity to Einstein's general relativity 62
Chapter 5 Schwarzschild Solution and its Consequences 65
5.1 The metric 65
5.2 The measurement of distance and time in general relativity 66
5.3 The event horizon, black holes and singularities 68
5.4 The tests of general relativity 78
Chapter 6 Gravitational Waves 83
6.1 Introduction 83
6.2 Linearized field equations 83
6.3 The energy issue and the pseudotensor 85
6.4 The energy localization hypothesis 86
Chapter 7 The Normal Scales of Physics and the Planck Scale93
7.1 The hierarchy of scales 93
7.2 The fundamental interactions of nature 95
7.3 The Planck scale and the issue of the quantization of gravity 96
7.4 Adding spin and charge to the Planck scale 97
7.5 Quantum limits, spectra, the value of α 100
Chapter 8 General Relativistic Cosmology 103
8.1 Sizes of astronomical elements 103
8.2 Early ideas about cosmology 104
8.3 Friedmann universes 108
8.4 The cosmological term 110
Chapter 9 Motion of the Stars in the Galaxy 115
9.1 Introduction 115
9.2 General relativistic effects on the stellar motions in galaxies 117
9.3 Modeling the observed galactic rotation curves 121
9.4 A velocity dispersion test for the presence of extra matter 130
9.5 Summary comments on rotation velocities of galaxies 131
Chapter 10 Clusters of Galaxies 135
10.1 Preliminary comments 135
10.2 Spherical dust collapse 136
10.3 Velocity of particles falling in vacuum toward a spherical concentration of mass 138
10.4 The velocity of dust in collapse 142
10.5 Observing an idealized galactic cluster 147
10.6 Current evidence for dark matter 154
Chapter 11 Closed Timelike Curves and Time Machines 161
11.1 The background 161
11.2 Creating closed timelike curves and Göet;del's spacetime 163
11.3 Re-examining the standard closed timelike curve interpretation 165
11.4 The role of our experience in nature 171
11.5 Gott's moving cosmic strings 172
Chapter 12 The Direction of Physics Research 179
Chapter 13 Summary with Concluding Commentary 187
Appendix A Critical Challenges and Our Replies 195
Appendix B Radial Velocity Derivation Details 213
Bibliography 217
Acknowledgements 225
Index 227
