Preface |
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ix | |
Constants |
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xiii | |
Notation |
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xv | |
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1 Newton's gravitational theory |
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1 | (46) |
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1.1 The law of universal gravitation |
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1 | (3) |
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1.2 Tests of the inverse-square law |
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4 | (7) |
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1.3 Gravitational potential |
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11 | (2) |
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1.4 Gravitational multipoles; quadrupole moment of the Sun |
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13 | (4) |
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1.5 Inertial and gravitational mass |
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17 | (2) |
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1.6 Tests of equality of gravitational and inertial mass |
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19 | (10) |
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29 | (5) |
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1.8 Tidal field as a local measure of gravitation |
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34 | (8) |
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42 | (3) |
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45 | (2) |
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2 The formalism of special relativity |
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47 | (48) |
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2.1 The spacetime of special relativity |
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48 | (7) |
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55 | (7) |
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62 | (2) |
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2.4 Energy-momentum tensor |
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64 | (7) |
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2.5 Relativistic electrodynamics |
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71 | (5) |
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2.6 Differential forms and exterior calculus |
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76 | (11) |
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87 | (7) |
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94 | (1) |
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3 The linear approximation |
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95 | (32) |
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3.1 The example of electromagnetism |
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95 | (6) |
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3.2 Linear field equations for gravitation |
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101 | (5) |
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3.3 Variational principle and equation of motion |
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106 | (6) |
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3.4 Nonrelativistic limit and Newton's theory |
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112 | (5) |
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3.5 Geometric interpretation; curved spacetime |
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117 | (6) |
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123 | (3) |
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126 | (1) |
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4 Applications of the linear approximation |
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127 | (55) |
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4.1 Field of a spherical mass |
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127 | (3) |
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4.2 Gravitational time dilation |
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130 | (8) |
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138 | (4) |
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142 | (7) |
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149 | (10) |
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4.6 Optics of gravitational lenses |
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159 | (5) |
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4.7 Field of a rotating mass; Lense-Thirring effect |
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164 | (6) |
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170 | (10) |
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180 | (2) |
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182 | (39) |
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182 | (5) |
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5.2 Interaction of particles with a gravitational wave |
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187 | (4) |
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5.3 Emission of gravitational radiation |
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191 | (5) |
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5.4 Emission by a vibrating quadrupole |
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196 | (3) |
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5.5 Emission by a rotating quadrupole |
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199 | (5) |
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5.6 Emission of bursts of gravitational radiation |
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204 | (4) |
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5.7 Detectors of gravitational radiation |
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208 | (7) |
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215 | (5) |
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220 | (1) |
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221 | (54) |
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6.1 General coordinates and tensors |
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223 | (3) |
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6.2 Parallel transport; covariant derivative |
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226 | (6) |
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232 | (4) |
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236 | (7) |
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6.5 Riemann curvature tensor |
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243 | (9) |
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6.6 Geodesic deviation and tidal forces; Fermi-Walker transport |
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252 | (5) |
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6.7 Differential forms in curved spacetime |
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257 | (5) |
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6.8 Isometries of spacetime; Killing vectors |
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262 | (6) |
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268 | (6) |
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274 | (1) |
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7 Einstein's gravitational theory |
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275 | (49) |
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7.1 General covariance and invariance; gauge transformations |
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276 | (8) |
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7.2 Einstein's field equation |
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284 | (4) |
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7.3 Another approach to Einstein's equation; cosmological term |
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288 | (5) |
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7.4 Schwarzschild solution and Birkhoff theorem |
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293 | (6) |
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7.5 Motion of planets; perihelion precession |
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299 | (6) |
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7.6 Propagation of light; gravitational redshift |
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305 | (4) |
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309 | (8) |
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317 | (5) |
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322 | (2) |
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8 Black holes and gravitational collapse |
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324 | (65) |
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8.1 Singularities and pseudosingularities |
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325 | (4) |
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8.2 The black hole and its horizon |
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329 | (6) |
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8.3 Maximal Schwarzschild geometry |
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335 | (8) |
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8.4 Kerr solution and Reissner-Nordstrøm solution |
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343 | (6) |
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8.5 Horizons and singularities of the rotating black hole |
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349 | (7) |
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8.6 Maximal Kerr geometry |
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356 | (4) |
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8.7 Black-hole thermodynamics; Hawking process |
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360 | (7) |
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8.8 Gravitational collapse and formation of black holes |
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367 | (8) |
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8.9 In search of black holes |
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375 | (6) |
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381 | (6) |
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387 | (2) |
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389 | (55) |
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9.1 Large-scale structure of the universe |
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390 | (2) |
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392 | (2) |
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9.3 Expansion of the universe; Hubble's law |
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394 | (7) |
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401 | (3) |
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9.5 Cosmic background radiation |
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404 | (4) |
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9.6 Mass density; dark mass |
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408 | (3) |
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9.7 Comoving coordinates; Robertson-Walker geometry |
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411 | (7) |
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9.8 Friedmann models (ρ ≠ 0, Λ = 0) |
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418 | (6) |
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9.9 Empty Lemaitre models (ρ = 0, Λ ≠ 0) |
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424 | (2) |
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9.10 Friedmann-Lemaitre models (ρ ≠ 0: Λ ≠ 0) |
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426 | (2) |
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9.11 Propagation of light; particle horizon |
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428 | (6) |
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9.12 Comparison of theory and observation |
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434 | (3) |
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437 | (5) |
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442 | (2) |
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444 | (33) |
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10.1 Temperature of the early universe |
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445 | (6) |
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10.2 Nucleosynthesis; abundance of primordial helium |
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451 | (5) |
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10.3 Density perturbations; Jeans mass |
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456 | (6) |
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462 | (11) |
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473 | (3) |
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476 | (1) |
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Appendix: Variational principle and energy-momentum tensor |
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477 | (20) |
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A.1 Lagrange equations for a system of particles |
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477 | (2) |
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A.2 Lagrange equations for fields |
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479 | (3) |
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A.3 Energy-momentum tensor |
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482 | (4) |
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A.4 Variational principle for Einstein's equations |
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486 | (5) |
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A.5 Flux theorem and its implications for gravitational and inertial mass |
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491 | (5) |
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496 | (1) |
Answers to even-numbered problems |
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497 | (6) |
Index |
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503 | |