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

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
 
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