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viii | |
Preface |
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xi | |
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1 Foundations of Newtonian gravity |
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1 | (62) |
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1 | (2) |
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1.2 Equations of Newtonian gravity |
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3 | (4) |
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1.3 Newtonian field equation |
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7 | (3) |
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1.4 Equations of hydrodynamics |
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10 | (17) |
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1.5 Spherical and nearly spherical bodies |
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27 | (18) |
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1.6 Motion of extended fluid bodies |
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45 | (15) |
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1.7 Bibliographical notes |
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60 | (1) |
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61 | (2) |
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2 Structure of self-gravitating bodies |
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63 | (75) |
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2.1 Equations of internal structure |
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64 | (2) |
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2.2 Equilibrium structure of a spherical body |
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66 | (23) |
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2.3 Rotating self-gravitating bodies |
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89 | (16) |
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2.4 General theory of deformed bodies |
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105 | (14) |
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2.5 Tidally deformed bodies |
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119 | (16) |
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2.6 Bibliographical notes |
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135 | (1) |
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135 | (3) |
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3 Newtonian orbital dynamics |
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138 | (51) |
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3.1 Celestial mechanics from Newton to Einstein |
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138 | (2) |
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3.2 Two bodies: Kepler's problem |
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140 | (14) |
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3.3 Perturbed Kepler problem |
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154 | (7) |
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3.4 Case studies of perturbed Keplerian motion |
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161 | (12) |
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173 | (8) |
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3.6 Lagrangian formulation of Newtonian dynamics |
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181 | (3) |
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3.7 Bibliographical notes |
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184 | (1) |
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185 | (4) |
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189 | (28) |
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189 | (14) |
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4.2 Relativistic hydrodynamics |
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203 | (5) |
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208 | (3) |
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4.4 Point particles in spacetime |
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211 | (3) |
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4.5 Bibliographical notes |
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214 | (1) |
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214 | (3) |
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217 | (73) |
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5.1 Gravitation as curved spacetime |
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217 | (8) |
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5.2 Mathematics of curved spacetime |
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225 | (18) |
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5.3 Physics in curved spacetime |
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243 | (7) |
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5.4 Einstein field equations |
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250 | (2) |
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252 | (12) |
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5.6 Spherical bodies and Schwarzschild spacetime |
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264 | (20) |
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5.7 Bibliographical notes |
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284 | (1) |
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285 | (5) |
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6 Post-Minkowskian theory: Formulation |
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290 | (38) |
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6.1 Landau--Lifshitz formulation of general relativity |
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291 | (10) |
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6.2 Relaxed Einstein equations |
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301 | (7) |
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6.3 Integration of the wave equation |
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308 | (17) |
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6.4 Bibliographical notes |
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325 | (1) |
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326 | (2) |
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7 Post-Minkowskian theory: Implementation |
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328 | (43) |
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329 | (12) |
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341 | (3) |
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7.3 Second iteration: Near zone |
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344 | (17) |
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7.4 Second iteration: Wave zone |
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361 | (4) |
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7.5 Bibliographical notes |
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365 | (1) |
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366 | (5) |
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8 Post-Newtonian theory: Fundamentals |
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371 | (43) |
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8.1 Equations of post-Newtonian theory |
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371 | (7) |
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8.2 Classic approach to post-Newtonian theory |
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378 | (3) |
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8.3 Coordinate transformations |
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381 | (19) |
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8.4 Post-Newtonian hydrodynamics |
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400 | (10) |
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8.5 Bibliographical notes |
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410 | (1) |
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410 | (4) |
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9 Post-Newtonian theory: System of isolated bodies |
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414 | (66) |
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9.1 From fluid configurations to isolated bodies |
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414 | (9) |
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423 | (8) |
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9.3 Motion of isolated bodies |
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431 | (14) |
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9.4 Motion of compact bodies |
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445 | (9) |
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9.5 Motion of spinning bodies |
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454 | (20) |
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474 | (4) |
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9.7 Bibliographical notes |
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478 | (1) |
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479 | (1) |
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10 Post-Newtonian celestial mechanics, astrometry and navigation |
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480 | (59) |
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10.1 Post-Newtonian two-body problem |
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481 | (11) |
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10.2 Motion of light in post-Newtonian gravity |
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492 | (17) |
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10.3 Post-Newtonian gravity in timekeeping and navigation |
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509 | (11) |
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520 | (14) |
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10.5 Bibliographical notes |
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534 | (1) |
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535 | (4) |
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539 | (85) |
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11.1 Gravitational-wave field and polarizations |
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540 | (10) |
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11.2 The quadrupole formula |
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550 | (14) |
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11.3 Beyond the quadrupole formula: Waves at 1.5PN order |
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564 | (38) |
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11.4 Gravitational waves emitted by a two-body system |
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602 | (13) |
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11.5 Gravitational waves and laser interferometers |
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615 | (3) |
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11.6 Bibliographical notes |
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618 | (1) |
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619 | (5) |
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12 Radiative losses and radiation reaction |
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624 | (75) |
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12.1 Radiation reaction in electromagnetism |
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625 | (9) |
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12.2 Radiative losses in gravitating systems |
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634 | (7) |
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12.3 Radiative losses in slowly-moving systems |
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641 | (9) |
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12.4 Astrophysical implications of radiative losses |
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650 | (7) |
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12.5 Radiation-reaction potentials |
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657 | (9) |
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12.6 Radiation reaction of fluid systems |
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666 | (7) |
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12.7 Radiation reaction of N-body systems |
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673 | (3) |
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12.8 Radiation reaction in alternative gauges |
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676 | (7) |
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12.9 Orbital evolution under radiation reaction |
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683 | (9) |
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12.10 Bibliographical notes |
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692 | (2) |
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694 | (5) |
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13 Alternative theories of gravity |
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699 | (61) |
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13.1 Metric theories and the strong equivalence principle |
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700 | (3) |
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13.2 Parameterized post-Newtonian framework |
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703 | (18) |
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13.3 Experimental tests of gravitational theories |
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721 | (11) |
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13.4 Gravitational radiation in alternative theories of gravity |
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732 | (7) |
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13.5 Scalar--tensor gravity |
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739 | (16) |
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13.6 Bibliographical notes |
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755 | (1) |
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756 | (4) |
References |
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760 | (11) |
Index |
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771 | |