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Part I RELATIVITY Metric Description of Spacetime |
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Introduction and overview |
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3 | (11) |
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Relativity as a coordinate symmetry |
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5 | (3) |
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From Newtonian relativity to aether |
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5 | (1) |
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6 | (1) |
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Coordinate symmetry transformations |
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7 | (1) |
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New kinematics and dynamics |
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7 | (1) |
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GR as a gravitational field theory |
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8 | (6) |
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Einstein's motivations for the general theory |
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8 | (2) |
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10 | (1) |
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Mathematical language of relativity |
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11 | (1) |
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GR is the framework for cosmology |
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12 | (1) |
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12 | (2) |
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Special relativity and the flat spacetime |
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14 | (24) |
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14 | (5) |
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14 | (2) |
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Newtonian physics and Galilean symmetry |
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16 | (1) |
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Electrodynamics and Lorentz symmetry |
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17 | (1) |
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Velocity addition rule amended |
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18 | (1) |
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The new kinematics of space and time |
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19 | (5) |
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Relativity of spatial congruity |
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20 | (1) |
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Relativity of simultaneity---the new kinematics |
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20 | (2) |
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The invariant space--time interval |
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22 | (2) |
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Geometric formulation of SR |
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24 | (14) |
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General coordinates and the metric tensor |
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24 | (4) |
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Derivation of Lorentz transformation |
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28 | (2) |
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30 | (2) |
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Time-dilation and length contraction |
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32 | (3) |
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35 | (1) |
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35 | (3) |
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The principle of equivalence |
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38 | (17) |
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Newtonian gravitation potential---a review |
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38 | (1) |
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39 | (4) |
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Inertial mass vs. gravitational mass |
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40 | (1) |
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41 | (2) |
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Implications of the strong EP |
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43 | (12) |
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Gravitational redshift and time dilation |
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43 | (5) |
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Light ray deflection calculated |
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48 | (3) |
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Energy considerations of a gravitating light pulse |
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51 | (1) |
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Einstein's inference of a curved spacetime |
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52 | (1) |
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53 | (1) |
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53 | (2) |
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Metric description of a curved space |
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55 | (16) |
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56 | (1) |
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57 | (6) |
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Geodesic as the shortest curve |
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59 | (2) |
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Local Euclidean coordinates |
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61 | (2) |
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63 | (8) |
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63 | (1) |
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Spaces with constant curvature |
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64 | (2) |
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Curvature measures deviation from Euclidean relations |
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66 | (2) |
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68 | (1) |
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69 | (2) |
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GR as a geometric theory of gravity - I |
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71 | (16) |
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71 | (4) |
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EP physics and a warped spacetime |
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73 | (1) |
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Curved spacetime as gravitational field |
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74 | (1) |
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Geodesic equation as GR equation of motion |
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75 | (4) |
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76 | (2) |
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Gravitational redshift revisited |
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78 | (1) |
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The curvature of spacetime |
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79 | (8) |
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Tidal force as the curvature of spacetime |
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80 | (3) |
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The GR field equation described |
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83 | (2) |
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85 | (1) |
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85 | (2) |
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Spacetime outside a spherical star |
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87 | (28) |
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Description of Schwarzschild spacetime |
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87 | (5) |
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Spherically symmetric metric tensor |
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88 | (2) |
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90 | (2) |
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92 | (5) |
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Light ray deflection revisited |
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93 | (1) |
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93 | (4) |
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Precession of Mercury's perihelion |
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97 | (5) |
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102 | (13) |
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Singularities of the Schwarzschild metric |
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102 | (1) |
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Time measurements in the Schwarzschild spacetime |
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102 | (3) |
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Lightcones of the Schwarzschild black hole |
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105 | (3) |
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Orbit of an object around a black hole |
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108 | (1) |
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Physical reality of black holes |
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108 | (3) |
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111 | (1) |
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112 | (3) |
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The homogeneous and isotropic universe |
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115 | (21) |
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116 | (9) |
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Matter distribution on the cosmic distance scale |
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116 | (1) |
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Cosmological redshift: Hubble's law |
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116 | (4) |
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120 | (1) |
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Dark matter and mass density of the universe |
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121 | (4) |
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The cosmological principle |
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125 | (2) |
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The Robertson---Walker metric |
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127 | (9) |
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Proper distance in the RW geometry |
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129 | (1) |
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Redshift and luminosity distance |
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130 | (3) |
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133 | (1) |
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134 | (2) |
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The expanding universe and thermal relics |
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136 | (29) |
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137 | (5) |
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The quasi-Newtonian interpretation |
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139 | (3) |
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Time evolution of model universes |
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142 | (3) |
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145 | (4) |
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Scale-dependence of radiation's temperature |
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145 | (2) |
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Different thermal equilibrium stages |
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147 | (2) |
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Primordial nucleosynthesis |
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149 | (3) |
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Photon decoupling and the CMB |
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152 | (13) |
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Universe became transparent to photons |
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153 | (1) |
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The discovery of CMB radiation |
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154 | (1) |
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Photons, neutrinos, and the radiation--matter equality time |
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155 | (4) |
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CMB temperature fluctuation |
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159 | (3) |
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162 | (1) |
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163 | (2) |
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Inflation and the accelerating universe |
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165 | (32) |
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The cosmological constant |
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166 | (4) |
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Vacuum energy as source of gravitational repulsion |
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167 | (1) |
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168 | (2) |
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170 | (8) |
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Initial conditions for the standard big bang model |
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171 | (2) |
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173 | (2) |
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Inflation and the conditions it left behind |
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175 | (3) |
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CMB anisotropy and evidence for k = 0 |
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178 | (5) |
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Three regions of the angular power spectrum |
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179 | (2) |
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The primary peak and spatial geometry of the universe |
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181 | (2) |
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The accelerating universe in the present epoch |
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183 | (6) |
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Distant supernovae and the 1998 discovery |
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184 | (3) |
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Transition from deceleration to acceleration |
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187 | (2) |
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189 | (8) |
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193 | (1) |
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193 | (4) |
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Part III RELATIVITY Full Tensor Formulation |
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Tensors in special relativity |
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197 | (18) |
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General coordinate systems |
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197 | (3) |
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Four-vectors in Minkowski spacetime |
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200 | (5) |
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Manifestly covariant formalism for E&M |
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205 | (3) |
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The electromagnetic field tensor |
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205 | (3) |
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Electric charge conservation |
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208 | (1) |
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208 | (7) |
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213 | (1) |
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213 | (2) |
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Tensors in general relativity |
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215 | (18) |
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Derivatives in a curved space |
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215 | (7) |
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General coordinate transformations |
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216 | (2) |
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Covariant differentiation |
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218 | (2) |
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Christoffel symbols and metric tensor |
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220 | (2) |
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222 | (3) |
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Component changes under parallel transport |
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222 | (2) |
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The geodesic as the straightest possible curve |
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224 | (1) |
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Riemannian curvature tensor |
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225 | (8) |
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The curvature tensor in an n-dimensional space |
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226 | (2) |
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Symmetries and contractions of the curvature tensor |
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228 | (2) |
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230 | (1) |
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231 | (2) |
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GR as a geometric theory of gravity - II |
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233 | (17) |
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The principle of general covariance |
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233 | (3) |
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Geodesic equation from SR equation of motion |
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235 | (1) |
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236 | (3) |
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Finding the relativistic gravitational field equation |
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236 | (1) |
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Newtonian limit of the Einstein equation |
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237 | (2) |
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The Schwarzschild exterior solution |
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239 | (5) |
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The Einstein equation for cosmology |
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244 | (6) |
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Solution for a homogeneous and isotropic 3D space |
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244 | (2) |
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246 | (1) |
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Einstein equation with a cosmological constant term |
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247 | (1) |
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248 | (1) |
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248 | (2) |
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Linearized theory and gravitational waves |
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250 | (21) |
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The linearized Einstein theory |
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251 | (3) |
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The coordinate change called gauge transformation |
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252 | (1) |
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The wave equation in the Lorentz gauge |
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253 | (1) |
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Plane waves and the polarization tensor |
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254 | (1) |
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Gravitational wave detection |
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255 | (4) |
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Effect of gravitational waves on test particles |
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255 | (2) |
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Gravitational wave interferometers |
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257 | (2) |
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Evidence for gravitational wave |
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259 | (12) |
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Energy flux in linearized gravitational waves |
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260 | (2) |
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Emission of gravitational radiation |
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262 | (2) |
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Binary pulsar PSR 1913+16 |
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264 | (4) |
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268 | (1) |
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269 | (2) |
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271 | (12) |
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A.1 The twin paradox (Section 2.3.4) |
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271 | (4) |
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A.2 A glimpse of advanced topics in black hole physics (Section 6.4) |
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275 | (4) |
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A.3 False vacuum and hidden symmetry (Section 9.2.2) |
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279 | (1) |
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A.4 The problem of Λ as quantum vacuum energy (Section 9.4) |
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280 | (3) |
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B Answer keys to review questions |
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283 | (10) |
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C Solutions of selected problems |
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293 | (37) |
References |
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330 | (3) |
Bibliography |
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333 | (2) |
Index |
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335 | |