| Preface to the Dover Edition |
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xi | |
| Preface |
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xiii | |
| Notation |
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xvii | |
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1 | (12) |
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The Lorentz Transformations as Viewed by Einstein |
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1 | (6) |
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7 | (4) |
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11 | (2) |
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2 Clocks and Gravitational Potential |
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13 | (14) |
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Gravitation, Acceleration, and the Principle of Equivalence |
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13 | (3) |
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The Pseudo-Riemannian Structure of Space-Time |
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16 | (4) |
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20 | (5) |
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Is Gravitation Governed by a Single Potential? |
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25 | (2) |
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3 A Heuristic Derivation of Einstein's Equations |
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27 | (8) |
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27 | (2) |
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29 | (2) |
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31 | (4) |
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4 The Geometry of Einstein's Equations |
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35 | (11) |
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Curvature in a Pseudo-Riemannian M4 |
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35 | (4) |
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39 | (2) |
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The Gauss Equations in M4 |
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41 | (1) |
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A Geometric Form of Einstein's Equations |
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42 | (4) |
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5 The Schwarzschild Solution |
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46 | (10) |
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Schwarzschild Coordinates |
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46 | (1) |
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Embedding the Spatial Section |
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47 | (3) |
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The Gravitational Potential and g00 |
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50 | (2) |
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The Schwarzschild Singularity |
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52 | (1) |
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53 | (3) |
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6 The Classical Motion of a Continuum |
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56 | (15) |
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Lie Derivatives, Interior Products, and the Variation of Integrals |
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56 | (8) |
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The Cauchy Stress Tensor in Classical Mechanics |
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64 | (5) |
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The Stress-Energy-Momentum Tensor |
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69 | (2) |
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7 The Relativistic Equations of Motion |
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71 | (19) |
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Fermi Transport and the Relative Velocity Vector |
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71 | (3) |
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Vorticity, Strain, and Expansion |
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74 | (4) |
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Shear and the Stress Tensor for a Viscous Fluid |
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78 | (2) |
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Divergence of the Einstein Tensor: Gravitational "Force" |
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80 | (2) |
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82 | (3) |
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Geodesics and Constants of Motion |
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85 | (3) |
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88 | (2) |
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8 Light Rays and Fermat's Principle |
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90 | (9) |
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Fermat's Principle of Stationary Time |
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90 | (3) |
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Geodesics in Conformally Related Metrics |
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93 | (2) |
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95 | (4) |
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9 Electromagnetism in Three-Space and Minkowski Space |
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99 | (16) |
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Twisted Forms and the Vector Product |
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99 | (1) |
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E, B, and the (Heaviside-) Lorentz Force in Three-Space |
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100 | (2) |
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Electromagnetism in Minkowski Space |
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102 | (1) |
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Integration of Twisted Forms |
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103 | (2) |
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The Charge-Current Three-Form in Minkowski Space |
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105 | (1) |
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106 | (2) |
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The Laws of Gauss and Ampere-Maxwell |
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108 | (4) |
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Faraday's Law and the Absence of Magnetic Monopoles |
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112 | (3) |
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10 Electromagnetism in General Relativity |
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115 | (13) |
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115 | (3) |
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The Electromagnetic Stress-Energy-Momentum Tensor |
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118 | (3) |
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121 | (3) |
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Conformal Invariance of Maxwell's Equations |
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124 | (1) |
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Poisson's Equation in a Static Universe |
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125 | (2) |
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127 | (1) |
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128 | (11) |
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Curvature of World Lines and Gravitational Force Potential |
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128 | (2) |
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The Schwarzschild Interior Solution |
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130 | (4) |
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The Oppenheimer-Volkoff Equation |
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134 | (5) |
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139 | (28) |
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The Einstein Static Universe |
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139 | (2) |
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The Friedmann Cosmology: Assumptions |
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141 | (3) |
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The Friedmann Cosmology: The Solution |
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144 | (5) |
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The (Landau-) Raychaudhuri Equation |
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149 | (3) |
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The Geometry of a Vorticity-Free Flow |
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152 | (1) |
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A Generalized Poisson Equation for Vorticity-Free Flows |
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152 | (3) |
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General Vorticity-Free Cosmologies: The Influence of Curvature on Expansion |
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155 | (2) |
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General Vorticity-Free Cosmologies: Singularities |
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157 | (2) |
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General Vorticity-Free Cosmologies: Closed Spatial Universes |
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159 | (8) |
| References |
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167 | (2) |
| Index |
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169 | |
