General Relativistic Dynamics: Extending Einstein's Legacy Throughout The Universe

by Fred Isaac Cooperstock

Overview

This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown “dark matter” required in models based on Newtonian gravity.Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction to relativity for readers who have little or no background in the subject. Hermann Bondi's very transparent approach to special relativity is expanded to resolve the “twin paradox” using only elementary mathematics. In later chapters, general relativity is used to extend the concept of the Planck scale, to address the role of the cosmological term and to analyze the concept of “time machines”.

Product Details

ISBN-13:	9789814271165
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/30/2009
Pages:	244
Product dimensions:	6.00(w) x 9.00(h) x 0.80(d)

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