Preface to the third edition |
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ix | |
Preface to the second edition |
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xi | |
Preface to the first edition |
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xiii | |
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1 | (32) |
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1.1 Fundamental principles of special relativity theory (SR) |
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1 | (2) |
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1.2 Definition of an inertial observer in SR |
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3 | (1) |
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4 | (1) |
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5 | (1) |
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1.5 Construction of the coordinates used by another observer |
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6 | (3) |
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1.6 Invariance of the interval |
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9 | (4) |
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13 | (4) |
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1.8 Particularly important results |
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17 | (4) |
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1.9 The Lorentz transformation |
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21 | (2) |
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1.10 The velocity-addition law |
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23 | (1) |
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1.11 Paradoxes and physical intuition |
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23 | (1) |
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24 | (1) |
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1.13 Appendix: The twin `paradox' dissected |
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25 | (8) |
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27 | (6) |
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2 Vector analysis in special relativity |
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33 | (23) |
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2.1 Definition of a vector |
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33 | (3) |
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36 | (5) |
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41 | (1) |
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2.4 The four-momentum and its conservation |
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42 | (2) |
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44 | (2) |
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46 | (2) |
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48 | (1) |
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49 | (7) |
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50 | (6) |
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3 Tensor analysis in special relativity |
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56 | (28) |
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56 | (1) |
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3.2 Definition of tensors |
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56 | (2) |
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3.3 The (0/1) tensors: one-forms |
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58 | (4) |
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3.4 Gradient of a function is a one-form |
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62 | (4) |
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66 | (2) |
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3.6 Metric as a mapping of vectors into one-forms |
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68 | (4) |
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3.7 Finally: (M/N) tensors |
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72 | (1) |
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3.8 Index `raising' and `lowering' |
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73 | (2) |
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3.9 Differentiation of tensors |
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75 | (1) |
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76 | (8) |
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76 | (8) |
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4 Perfect fluids in special relativity |
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84 | (27) |
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84 | (1) |
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4.2 Dust: the number-flux vector N |
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85 | (3) |
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4.3 One-forms and surfaces |
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88 | (3) |
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4.4 Dust again: the stress-energy tensor |
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91 | (2) |
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93 | (5) |
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4.6 Conservation of energy-momentum |
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98 | (2) |
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100 | (3) |
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4.8 Importance for general relativity |
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103 | (1) |
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104 | (2) |
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106 | (5) |
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106 | (5) |
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111 | (30) |
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5.1 On the relation of gravitation to curvature |
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111 | (7) |
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5.2 Tensor algebra in polar coordinates |
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118 | (6) |
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5.3 Tensor calculus in polar coordinates |
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124 | (6) |
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5.4 Christoffel symbols and the metric |
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130 | (4) |
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134 | (4) |
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138 | (1) |
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138 | (3) |
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138 | (3) |
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141 | (29) |
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6.1 Differentiable manifolds and tensors |
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141 | (2) |
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143 | (6) |
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6.3 Covariant differentiation on a general manifold |
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149 | (3) |
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6.4 Parallel transport, geodesies, and curvature |
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152 | (4) |
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156 | (6) |
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6.6 Bianchi identities; Ricci and Einstein tensors |
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162 | (2) |
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6.7 Curvature in perspective |
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164 | (1) |
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165 | (5) |
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165 | (5) |
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7 Physics in a curved spacetime |
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170 | (13) |
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7.1 The transition from differential geometry to gravity |
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170 | (4) |
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7.2 Physics in slightly curved spacetimes |
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174 | (2) |
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176 | (1) |
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177 | (3) |
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180 | (3) |
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180 | (3) |
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8 The Einstein field equations |
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183 | (19) |
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8.1 Purpose and justification of the field equations |
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183 | (3) |
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186 | (2) |
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8.3 Einstein's equations for weak gravitational fields |
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188 | (4) |
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8.4 Newtonian gravitational fields |
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192 | (4) |
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196 | (6) |
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197 | (5) |
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9 Fundamentals of gravitational radiation |
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202 | (65) |
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9.1 The role of general relativity in the physical Universe |
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202 | (1) |
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9.2 The propagation of gravitational waves |
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203 | (10) |
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9.3 The detection of gravitational waves |
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213 | (17) |
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9.4 The generation of gravitational waves |
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230 | (9) |
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9.5 The energy carried away by gravitational waves |
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239 | (8) |
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247 | (6) |
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253 | (14) |
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255 | (12) |
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10 Spherical solutions for stars |
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267 | (29) |
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10.1 Coordinates for spherically symmetric spacetimes |
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267 | (2) |
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10.2 Static spherically symmetric spacetimes |
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269 | (2) |
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10.3 Static perfect-fluid Einstein equations |
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271 | (2) |
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10.4 The exterior geometry |
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273 | (1) |
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10.5 The interior structure of the star |
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274 | (2) |
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10.6 Exact interior solutions |
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276 | (4) |
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10.7 Realistic stars and gravitational collapse |
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280 | (11) |
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291 | (5) |
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292 | (4) |
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11 Schwarzschild geometry and black holes |
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296 | (64) |
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11.1 Trajectories in the Schwarzschild spacetime |
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296 | (19) |
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11.2 Nature of the surface r = 2M |
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315 | (7) |
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322 | (15) |
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11.4 Real black holes in astronomy |
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337 | (8) |
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345 | (5) |
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350 | (10) |
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352 | (8) |
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12 Gravitational wave astronomy |
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360 | (55) |
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360 | (2) |
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12.2 Astrophysical sources of gravitational waves |
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362 | (11) |
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12.3 Finding weak signals in noise: what is a detection? |
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373 | (23) |
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12.4 The first L1GO and Virgo detections |
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396 | (10) |
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406 | (9) |
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407 | (8) |
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415 | (53) |
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415 | (3) |
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13.2 Cosmological kinematics: observing our expanding Universe |
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418 | (20) |
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13.3 Cosmological dynamics: understanding the expanding Universe |
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438 | (9) |
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13.4 Physical cosmology: the evolution of the Universe we observe |
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447 | (15) |
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462 | (6) |
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463 | (5) |
Appendix A Summary of linear algebra |
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468 | (4) |
References |
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472 | (19) |
Index |
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491 | |