| Preface and Introduction |
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xi | |
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I Mathematical Preliminaries |
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1 | (18) |
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1 Tensors in Amorphous Spaces |
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3 | (8) |
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3 | (1) |
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3 | (4) |
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1.3 Algebraic Operations with Tensors |
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7 | (2) |
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9 | (2) |
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2 Tensors in Riemann Spaces |
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11 | (8) |
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11 | (2) |
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13 | (1) |
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14 | (1) |
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15 | (4) |
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II Introduction to General Relativity |
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19 | (42) |
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21 | (14) |
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21 | (1) |
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3.2 Energy-Momentum Tensor |
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22 | (2) |
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3.3 Tij for the Electromagnetic Field |
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24 | (1) |
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3.4 Einstein's Field Equations |
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25 | (2) |
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3.5 Introducing the Cosmological Constant |
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27 | (2) |
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3.6 Reduction of GRT into Newtonian Physics |
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29 | (3) |
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3.7 The Geodesics Equation - a Derivation |
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32 | (1) |
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3.8 Gravitational Radiation |
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33 | (2) |
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4 Schwarzschild's Metric and Classical Experimental Tests |
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35 | (16) |
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4.1 Spherically Symmetric Metrics |
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35 | (5) |
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4.2 The Motion of Planets and Perihelion Precession |
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40 | (4) |
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4.3 Propagation of Light near Gravitational Fields |
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44 | (2) |
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4.4 Spectral Displacement due to Gravitational Cause |
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46 | (1) |
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4.5 Other Verifications of the GRT |
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47 | (4) |
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5 Complements of Tensor Calculus and General Relativity (Optional Study) |
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51 | (10) |
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5.1 Orthogonal Transformations and Cartesian Tensors |
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51 | (2) |
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5.2 Parallel Transport in Riemann Space |
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53 | (2) |
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5.3 Fermi-Walker's Transport |
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55 | (1) |
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55 | (3) |
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58 | (1) |
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5.6 Stationary and Static Fields |
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59 | (2) |
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III Introduction to Relativistic Cosmology |
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61 | (44) |
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6 Digression into Philosophical and Mathematical Matters (Optional Study) |
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63 | (16) |
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6.1 Newtonian Concepts of Space and Time |
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63 | (1) |
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6.2 Objections to Newton's Cosmology |
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64 | (2) |
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66 | (2) |
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6.4 The Potential for Gravitation |
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68 | (3) |
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6.5 Equivalence Principle |
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71 | (2) |
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6.6 The principles of (General) Relativity, Covariance, and Simplicity |
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73 | (1) |
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6.7 Principles of "cosmic time" and "correspondence" |
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74 | (3) |
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6.8 Revisiting Mach's Principle |
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77 | (2) |
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7 Introductory Cosmological Models |
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79 | (26) |
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7.1 Derivation of the Homogeneous and Isotropic Metric |
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79 | (3) |
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7.2 Einstein's Field Equations for Cosmology |
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82 | (4) |
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7.3 Constant Deceleration Parameter Models |
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86 | (2) |
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7.4 Cosmological Red-Shift |
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88 | (2) |
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90 | (1) |
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7.6 Cosmological Model for Large Lambda |
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90 | (2) |
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92 | (1) |
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7.8 Planck's Universe and the A-problem |
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93 | (2) |
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7.9 Raychaudhuri's Equation and an Alternative Form |
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95 | (3) |
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7.10 Geodesics for Photons, Particles, and Tachyons in Robertson-Walker's Cosmology |
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98 | (3) |
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7.11 Energy of Robertson-Walker's Universe |
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101 | (1) |
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7.12 The Zero-Total Energy Density of the Universe |
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102 | (1) |
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7.13 The Cosmological Newtonian Limit of General Relativity |
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103 | (2) |
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105 | (74) |
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8 The Pioneers Anomaly and a Machian Universe |
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107 | (30) |
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8.1 Brief History of the Pioneers Anomaly |
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107 | (1) |
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8.2 The Zero-Total Energy Machian Universe |
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107 | (11) |
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8.3 Dirac's LNH with Time-Varying Fundamental "Constants" |
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118 | (6) |
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8.4 On Sciama's Machian Origin of Inertia |
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124 | (6) |
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8.5 Sciama's Machian Universe |
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130 | (4) |
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8.6 Exact Brans-Dicke Relation and Variable Speed of Light |
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134 | (3) |
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9 Relativistic Cosmology and the Pioneers Anomaly |
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137 | (22) |
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9.1 Generalised Robertson-Walker's Metric: Rotation Plus Expansion |
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137 | (5) |
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9.2 Generalised Robertson-Walker's Metric: Rotation Plus Expansion - II |
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142 | (3) |
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9.3 The Pioneers Anomaly and a Machian General Relativistic Model |
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145 | (10) |
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9.4 General Relativistic Cosmological Models with Pioneers Anomaly |
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155 | (2) |
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9.5 The Fundamental Theorem for the Pioneers Anomaly Solution in General Relativity |
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157 | (1) |
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9.6 The Pioneers Anomaly Solution with Universal Spin Conservation in General Relativity |
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158 | (1) |
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10 The Pioneers Anomaly and Several Relativistic Theories |
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159 | (16) |
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10.1 On Schwarzschild's and Robertson--Walker's Models |
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159 | (2) |
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10.2 Linearized Gravitomagnetism and Pioneers Anomaly |
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161 | (3) |
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10.3 The Pioneers Anomaly in a Variable Speed of Light Relativistic Cosmology |
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164 | (3) |
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10.4 Energy and Stability of Our Universe |
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167 | (3) |
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10.5 Frame-Dragging, Mach's Principle, and the Pioneers Anomalies |
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170 | (1) |
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10.6 Gravitational Larmor Theorem and the Pioneers Anomaly |
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171 | (4) |
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11 Possible Solutions to the Pioneers Anomaly |
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175 | (4) |
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11.1 Evidence on the Rotation of the Universe |
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175 | (1) |
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11.2 Thermal Emission as Deceleration Cause |
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175 | (1) |
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11.3 MOND (Modified Newtonian Dynamics) by Milgrom |
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176 | (1) |
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176 | (1) |
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176 | (3) |
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V Bibliography and References |
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179 | (22) |
| Index |
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201 | |
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