General Theory of Relativity (eBook)

Front Cover 1
General Theory of Relativity 4
Copyright Page 5
Table of Contents 6
Introduction 8
Acknowledgements 10
PART I: 12
CHAPTER I. The Principle of Equivalence 14
CHAPTER II. 
36 
CHAPTER III. 
73 
References 107
PART II: 110
NOTES ON EXTRACT 1 112
Chapter I. On the Hypotheses which Lie at the Bases of Geometry 118
Plan of the investigation 118
I. Notion of an n-ply extended magnitude 119
II. Measure-relations of which a manifoldness of n dimensions is capable on the assumption that lines have a length independent of position, and consequently that every line may be measured by every other 122
III. Application to Space 129
Synopsis 132
NOTES ON EXTRACT 2 135
Chapter 2. On the Space-theory of Matter 136
(Abstract) 136
NOTES ON EXTRACT 3 139
Chapter 3. On the Effect of Gravitation on the Propagation Light 140
§ 1. A Hypothesis on the Physical Nature of the Gravitational Field 140
§ 2. On the Weight of Energy 142
§ 3. Time and the Velocity of Light in the Gravitational Field 145
§ 4. Bending of Light-rays in the Gravitational Field 148
NOTES ON EXTRACT 4 151
Chapter 4. A The Foundations of General Relativity Theory 152
A. Fundamental Considerations on the Postulate of Relativity 153
C· Theory of the Gravitational Field 165
D. Material Phenomena 174
NOTES ON EXTRACT 5 185
Chapter 5. On the Motion of Particles in General Relativity Theory 186
1. Introduction 186
2. Notations 189
3. Lemma 191
4. Surface Integrals 193
5. The Method of Approximation 194
6. Field Equations and the Approximation Method 196
7. The Divergence Condition 198
8. The Surface Condition and the Equations of Motion 200
9. On the Choice of a Co-ordinate System 208
10. The Newtonian Approximation 211
11. Transition to the Next Approximation 214
12. Beyond the Newtonian Approximation 216
13. The Equations of Motion and the Co-ordinate Condition 219
References 230
NOTES ON EXTRACT 6 231
EXTRACT 6. 
232 
First Lecture: on Homogeneity, Covariance, and Relativity 232
NOTES ON EXTRACT 7 239
EXTRACT 7. Invariant Formulation of Gravitational Radiation Theory 240
1. Introduction 241
2. Nature of a Gravitational Wave Front 245
3. Canonical Forms for the Riemann tensor 251
4. Reduction of the Energy-momentum Pseudotensor 258
5. Examples 265
NOTES ON EXTRACT 8 269
Chapter 8. Gravitational Waves in General Relativity: VII. Waves from Axisymmetric Isolated Systems 270
PART A. GENERAL CONSIDERATIONS 271
1. Introduction 271
2. Causality 271
3. The Loss of Mass 273
4. Huygens's Principle and the Change of Wave Form 274
5. Method of Treatment 275
PART B. A SUITABLE CO-ORDINATE SYSTEM 279
1· The Character of the Metric 279
2. The Structure of the Field Equations 283
3. The Main Equations 284
4. The Outgoing Wave Condition 285
5. The Supplementary Conditions 289
6. The Static Case 289
7. The Curvature Tensor 290
PART C. PERMISSIBLE CO-ORDINATE TRANSFORMATIONS 292
1. Evaluation of the Transformations by Power Series 292
2. Rigorous Transformations of Minkowski Space 294
PART D. THE NATURE OF THE SOLUTIONS 296
1. News and Mass Loss 296
2. Linearized Form of the Equations 299
3. Non-radiative Motions 301
4. Construction of Solutions 303
5. The Reception of Gravitational Waves 305
6. The Classification of Time Variation 310
References 312
Appendix 313
NOTES ON EXTRACT 9 319
Chapter 9. On Continued Gravitational Contraction 320
NOTES ON EXTRACT 10 329
Chapter 1O. A Spinor Approach to General Relativity 330
1. Introduction 330
2. The Curvature Spinors 334
3. The Einstein Conditions 338
4. The Geometry and invariants of .ABCD 342
5. Analytic Solutions of Einstein's Equations 356
References 367
NOTES ON EXTRACT 11 369
Chapter 11. Gravitational Red-shift in Nuclear Resonance 370
Index 374