The Theory of Space, Time and Gravitation

The Theory of Space, Time and Gravitation

2nd Edition - January 1, 1964

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  • Author: V. Fock
  • eBook ISBN: 9781483184906

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Description

The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two inertial frames. The text then ponders on general tensor analysis, including permissible transformations for space and time coordinates, parallel transport of a vector, covariant differentiation, and basic properties of the curvature tensor. The publication examines the formulation of relativity theory in arbitrary coordinates and principles of the theory of gravitation. Topics include equations of mathematical physics in arbitrary coordinates; integral form of the conservation laws in arbitrary coordinates; variational principle and the energy tensor; and comparison with the statement of the problem in Newtonian theory. The manuscript is a dependable reference for readers interested in the theory of space, time, and gravitation.

Table of Contents


  • Translator's Preface

    Preface

    Introduction

    I. The Theory of Relativity

    1. Coordinates of Space and Time

    2. The Position of a Body in Space at a given Instant, in a Fixed Reference Frame

    3. The Law of Propagation of an Electromagnetic Wave Front

    4. Equations for Rays

    5. Inertial Frames of Reference

    6. The Basic Postulates of the Theory of Relativity

    7. The Galileo Transformations and the Need to Generalize them

    8. Proof of the Linearity of the Transformation Linking Two Inertial Frames

    9. Determination of the Coefficients of the Linear Transformations and of a Scale Factor

    10. Lorentz Transformations

    11. Determination of Distances and Synchronization of Clocks within One Inertial Reference Frame

    12. Time Sequence of Events in Different Reference Frames

    13. Comparison of Time Differences in Moving Reference Frames. The Doppler Effect

    14. Comparison of Clock Readings in Moving Reference Frames

    15. Comparison of Distances and Lengths in Moving Reference Frames

    16. Relative Velocity

    17. The Lobachevsky-Einstein Velocity Space

    II. The Theory of Relativity in Tensor Form

    18. Some Remarks on the Co variance of Equations

    19. Definition of a Tensor in Three Dimensions and some Remarks on Covariant Quantities

    20. Definition of a Four-dimensional Vector

    21. Four-dimensional Tensors

    22. Pseudo-Tensors

    23. Infinitesimal Lorentz Transformations

    24. The Transformation Laws for the Electromagnetic Field and the Covariance of Maxwell's Equations

    25. The Motion of a Charged Mass-Point in a given External Field

    26. Approximate Description of a System of Moving Point Charges

    27. Derivation of the Conservation Laws in the Mechanics of Point Systems

    28. The Tensor Character of the Integrals of Motion

    29. A Remark on the Conventional Formulation of the Conservation Laws

    30. The Vector of Energy-Current (Umov's Vector)

    31. The Mass Tensor

    31. A System of Equations for the Components of the Mass Tensor as Functions of the Field

    32. Examples of the Mass Tensor

    33. The Energy Tensor of the Electromagnetic Field

    34. Mass and Energy

    III. General Tensor Analysis

    35. Permissible Transformations for Space and Time Coordinates

    36. General Tensor Analysis and Generalized Geometry

    37. The Definitions of a Vector and of a Tensor. Tensor Algebra

    38. The Equation of a Geodesic

    39. Parallel Transport of a Vector

    40. Covariant Differentiation

    41. Examples of Co variant Differentiation

    42. The Transformation Law for Christoflel Symbols and the Locally Geodesic Coordinate System. Conditions for Transforming ds2 to a Form with Constant Coefficients

    43. The Curvature Tensor

    44. The Basic Properties of the Curvature Tensor

    IV. A Formulation of Relativity Theory in Arbitrary Coordinates

    45. Properties of Space-Time and Choice of Coordinates

    46. The Equations of Mathematical Physics in Arbitrary Coordinates

    47. A Variational Principle for the Maxwell-Lorentz System of Equations

    48. The Variational Principle and the Energy Tensor

    49. The Integral Form of the Conservation Laws in Arbitrary Coordinates

    49. Remark on the Relativity Principle and the Covariance of Equations

    V. The Principles of the Theory of Gravitation

    50. The Generalization of Galileo's Law

    51. The Square of the Interval in Newtonian Approximation

    52. Einstein's Gravitational Equations

    53. The Characteristics of Einstein's Equations. The Speed of Propagation of Gravitation

    54. A Comparison with the Statement of the Problem in Newtonian Theory. Boundary Conditions

    55. Solution of Einstein's Gravitational Equations in First Approximation and Determination of the Constant

    56. The Gravitational Equations in the Static Case and Conformal Space

    57. Rigorous Solution of the Gravitational Equations for a Single Concentrated Mass

    58. The Motion of the Perihelion of a Planet

    59. The Deflection of a Light Ray Passing Near the Sun

    60. A Variational Principle for the Equations of Gravitation

    61. On the Local Equivalence of Fields of Acceleration and of Gravitation

    62. On the Clock Paradox

    VI. The Law of Gravitation and the Laws of Motion

    63. The Equations of Free Motion for a Mass Point and their Connection with the Gravitational Equations

    64. General Statement of the Problem of the Motion of a System of Masses

    65. The Divergence of the Mass Tensor in Second Approximation

    66. The Approximate Form of the Mass Tensor for an Elastic Solid with Inclusion of the Gravitational Field

    67. Approximate Expressions for the Christoffel Symbols and Some Other Quantities

    68. Approximate Form of the Gravitational Equations

    69. The Connection between the Divergence of the Mass Tensor and the Quantities I

    70. The Equations of Motion and the Harmonic Conditions

    71. The Internal and the External Problems in the Mechanics of Systems of Bodies. Newton's Equations for Translational Motion

    72. Newton's Equations for Rotational Motion

    73. The Internal Structure of a Body. Liapunov's Equation

    74. Evaluation of some Integrals that Characterize the Internal Structure of a Body

    75. Transformation of the Integral Form of the Equations of Motion

    76. Evaluation of the Momentum in Second Approximation

    77. Evaluation of the Force

    78. The Equations of Translational Motion in Lagrangian Form

    79. The Integrals of the Equations of Motion for Systems of Bodies

    80. Additional Remarks on the Problem of the Motion of a System of Bodies. The Explicit Form of the Integrals of Motion for the Case of Non-Rotating Masses

    81. The Problem of Two Bodies of Finite Mass

    VII. Approximate Solutions, Conservation Laws and Some Questions of Principle

    82. The Gravitational Potentials for Non-Rotating Bodies (Spatial Components)

    83. The Gravitational Potentials for Non-Rotating Bodies (Mixed and Temporal Components)

    84. Gravitational Potentials at Large Distances from a System of Bodies (Spatial Components)

    85. Gravitational Potentials at Large Distances from a System of Bodies (Mixed and Temporal Components)

    86. Solution of the Wave Equation in the Wave Zone

    87. The Gravitational Potentials in the Wave Zone

    88. Some General Remarks on the Conservation Laws

    89. Formulation of the Conservation Laws

    90. The Emission of Gravitational Waves and its Role in the Energy Balance

    91. The Connection between the Conservation Laws for the Field and the Integrals of Mechanics

    92. The Uniqueness Theorem for the Wave Equation

    93. On the Uniqueness of the Harmonic Coordinate System

    94. Friedmann-Lobachevsky Space

    95. Theory of the Red Shift

    96. The Development of the Theory of Gravitation and of the Motion of Masses (A Critical Survey)

    Conclusion

    Appendix A. On The Derivation of the Lorentz Transformations

    Appendix B. Proof of the Uniqueness of the Energy Momentum Tensor of the Electromagnetic Field

    Appendix C. Proof of the Uniqueness of the Hydro-Dynamic Mass Tensor

    Appendix D. The Transformations of the Einstein Tensor

    Appendix E. The Characteristics of the Generalized D'Alembert Equation

    Appendix F. Integration of the Wave Front Equation

    Appendix G. Necessary and Sufficient Conditions for the Euclidean Character of Three-Dimensional Space

    References

    Index

Product details

  • No. of pages: 460
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483184906

About the Author

V. Fock

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