General Relativistic Dynamics: Extending Einstein's Legacy Throughout the UniverseThis 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 OC dark matterOCO 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 OC twin paradoxOCO 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 OC time machinesOCO. |
Contents
Chapter 1 Introduction | 1 |
Chapter 2 Essentials of Special Relativity | 11 |
Chapter 3 Bondis kCalculus Approach to Special Relativity | 31 |
Chapter 4 Essentials of General Relativity | 47 |
Chapter 5 Schwarzschild Solution and its Consequences | 65 |
Chapter 6 Gravitational Waves | 83 |
Chapter 7 The Normal Scales of Physics and the Planck Scale | 93 |
Chapter 8 General Relativistic Cosmology | 103 |
Chapter 11 Closed Timelike Curves and Time Machines | 161 |
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 |
| 227 | |
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Common terms and phrases
accelerated reference frame approach Cayla Chapter closed timelike curves cluster of galaxies components consider constant contravariant coordinate system covariant density distance distant observers distribution ds˛ dust dynamics Einstein equations Einstein field equations electromagnetic elements energy energy-momentum tensor essential existence exotic dark matter expressed F. I. Cooperstock fall-off field equations Figure flat four-vector free-fall functions galactic galactic rotation curves geodesic Gödel grav gravitational field gravitational waves hand side inertial issue light cone Lorentz mass mathematical metric tensor momentum motion nature Newtonian gravity noted photon Phys physicists physics Planck length Planck mass Planck scale plane quantization quantum radial radius region relativistic researchers result rotation curves scalar Schwarzschild seen singularity solution space spacelike spacetime interval spatial special relativity speed spherical stars surface symmetry test particle theory of gravity timelike coordinate timelike curves tion trajectory transformation universe V˛/c˛ vacuum vector velocity zero