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Description Einstein's Apple: Homogeneous Einstein Fields by Engelbert L Schucking and Eugene J Surowitz World Scientific Publishing Co | April 2015 | ISBN: 9814630071 | 300 pages | PDF | 14.7 mb http://www.amazon.com/Einste...instein-Fields/dp/9814630071 We lift a veil of obscurity from a branch of mathematical physics in a straightforward manner that can be understood by motivated and prepared undergraduate students as well as graduate students specializing in relativity. Our book on "Einstein Fields" clarifies Einstein's very first principle of equivalence (1907) that is the basis of his theory of gravitation. This requires the exploration of homogeneous Riemannian manifolds, a program that was suggested by Elie Cartan in "Riemannian Geometry in an Orthogonal Frame," a 2001 World Scientific publication. Einstein's first principle of equivalence, the key to his General Relativity, interprets homogeneous fields of acceleration as gravitational fields. The general theory of these "Einstein Fields" is given for the first time in our monograph and has never been treated in such exhaustive detail. This study has yielded significant new insights to Einstein's theory. The volume is heavily illustrated and is accessible to well-prepared undergraduate and graduate students as well as the professional physics community. CONTENTS Preface vii Table of Contents ix List of Figures xi 0. “The Happiest Thought of My Life” 1 1. Accelerated Frames 13 2. Torsion and Telemotion 28 3. Inertial and Gravitational Fields inMinkowski Spacetime 38 4. The Notion of Torsion 47 5. Homogeneous Fields on Two-dimensional Riemannian Manifolds 60 6. Homogeneous Vector Fields in N-dimensions 79 7. Homogeneous Fields on Three-dimensional Spacetimes: Elementary Cases 94 8. Proper Lorentz Transformations 111 9. Limits of Spacetimes 136 10. Homogeneous Fields inMinkowski Spacetimes 162 11. Euclidean Three-dimensional Spaces 182 12. Homogeneous Fields in Arbitrary Dimension 208 13. Summary 225 Appendix A. Basic Concepts 229 Appendix B. A Non-trivial Global Frame Bundle 240 Appendix C. Geodesics of the Poincar´e Half-Plane 244 Appendix D. Determination of Homogeneous Fields in Two-dimensional Riemannian Spaces 253 Appendix E. Space Expansion 256 Appendix F. The Reissner-Nordstrom Isotropic Field 258 Appendix G. The Cremona Transformation 262 Appendix H. Hessenberg’s “Vectorial Foundation of Differential Geometry” 265 Appendix K. Gravitation Is Torsion 269 Appendix R. References 274 Appendix X. Index 284 Appendix N. Notations and Conventions 300 Sharing Widget |