EINSTEIN'S APPLE: HOMOGENEOUS EINSTEIN FIELDS: Homogeneous Einstein Fields

by Engelbert L Schucking, Eugene J Surowitz

Overview

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.

Product Details

ISBN-13:	9789814630092
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	01/29/2015
Sold by:	Barnes & Noble
Format:	eBook
Pages:	316
File size:	24 MB
Note:	This product may take a few minutes to download.

Table of 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 in Minkowski 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 in Minkowski 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 Geodesies of the Poincaré 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