General relativistic dynamics : extending Einstein's legacy throughout the universe / Fred I. Cooperstock.

Includes bibliographical references (pages 217-224) and index.

ch. 1. Introduction -- ch. 2. Essentials of special relativity. 2.1. Basic principles. 2.2. The spacetime interval and the Lorentz transformation. 2.3. Lorentz contraction and time dilation. 2.4. Causality. 2.5. Transformation of velocity and the aberration of light. 2.6. Four-vectors and four-tensors. 2.7. Special relativistic dynamics. 2.8. Relativistic Doppler shift -- ch. 3. Bondi's k-calculus approach to special relativity. 3.1. Introduction. 3.2. Velocity-Doppler factor connection. 3.3. Composition law for velocities and Doppler factors. 3.4. Derivation of the Lorentz transformation. 3.5. The twin or clock paradox -- ch. 4. Essentials of general relativity. 4.1. The need for a new theory of gravity. 4.2. The principle of equivalence. 4.3. The metric tensor. 4.4. Basic tensor calculus-introduction. 4.5. Parallel transport, spacetime curvature and the Riemann tensor. 4.6. Geodesics. 4.7. Covariant conservation laws and the Einstein field equations. 4.8. Einstein-Maxwell equations and motion of a charged body in general relativity. 4.9. Summary of the steps from Newtonian gravity to Einstein's general relativity -- ch. 5. Schwarzschild solution and its consequences. 5.1. The metric. 5.2. The measurement of distance and time in general relativity. 5.3. The event horizon, black holes and singularities. 5.4. The tests of general relativity -- ch. 6. Gravitational waves. 6.1. Introduction. 6.2. Linearized field equations. 6.3. The energy issue and the pseudotensor. 6.4. The energy localization hypothesis -- ch. 7. The normal scales of physics and the Planck scale. 7.1. The hierarchy of scales. 7.2. The fundamental interactions of nature. 7.3. The Planck scale and the issue of the quantization of gravity. 7.4. Adding spin and charge to the Planck scale. 7.5. Quantum limits, spectra, the value of [symbol] -- ch. 8. General relativistic cosmology. 8.1. Sizes of astronomical elements. 8.2. Early ideas about cosmology. 8.3. Friedmann universes. 8.4. The cosmological term -- ch. 9. Motion of the stars in the galaxy. 9.1. Introduction. 9.2. General relativistic effects on the stellar motions in galaxies. 9.3. Modeling the observed galactic rotation curves. 9.4. A velocity dispersion test for the presence of extra matter. 9.5. Summary comments on rotation velocities of galaxies -- ch. 10. Clusters of galaxies. 10.1. Preliminary comments. 10.2. Spherical dust collapse. 10.3. Velocity of particles falling in vacuum toward a spherical concentration of mass. 10.4. The velocity of dust in collapse. 10.5. Observing an idealized galactic cluster. 10.6. Current evidence for dark matter -- ch. 11. Closed timelike curves and time machines. 11.1. The background. 11.2. Creating closed timelike curves and Gödel's spacetime. 11.3. Re-examining the standard closed timelike curve interpretation. 11.4. The role of our experience in nature. 11.5. Gott's moving cosmic strings -- ch. 12. The direction of physics research -- ch. 13. Summary with concluding commentary.

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."

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