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Einstein, A.1
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K. Johnston, D. McCarthy, B. Luzum, and G. Kaplan, Towards Models and Constants for Sub-Microarcsecond Astrometry, Proceedings of the IAU Colloquium 180 (U.S. Naval Observatory, Washington, D.C., 2000).
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edited by J.H. Lieske and V.K. Abalakin (Kluwer, Dordrecht)
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V.A. Brumberg, S.A. Klioner, and S.M. Kopeikin, in Inertial Coordinate System on the Sky, edited by J.H. Lieske and V.K. Abalakin (Kluwer, Dordrecht, 1990), pp. 229-240.
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Brumberg, V.A.1
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12
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33750359394
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note
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Exhaustive consideration of the problem of interaction of quadrupolar gravitational waves with electromagnetic signals in the approximation of geometric optics is given in [7] and [15], where results obtained by previous authors are critically discussed and examined.
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13
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33750376684
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note
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The speed of propagation of gravitational interaction can be different from the speed of light in alternative theories of gravitation. For more details see Ref. [14].
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17
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0001081566
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L. Bel, T. Damour, N. Deruelle, J. Ibanez, and J. Martin, Gen. Relativ. Gravit. 13, 963 (1981).
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Bel, L.1
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Deruelle, N.3
Ibanez, J.4
Martin, J.5
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18
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0003994923
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edited by N. Deruelle and T. Piran (North-Holland, Amsterdam)
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T. Damour, in Gravitational Radiation, edited by N. Deruelle and T. Piran (North-Holland, Amsterdam, 1983).
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Gravitational Radiation
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Damour, T.1
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19
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0002627368
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edited by S.W. Hawking and W. Israel (Cambridge University Press, Cambridge, England)
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T. Damour, in, 300 Years of Gravitation, edited by S.W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987), pp. 128-198.
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Damour, T.1
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24
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33750315957
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note
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This effect was first discussed by Skrotskii [25]. The most exhaustive treatment of the effect in the framework of the post-Newtonian approximation was given recently by Klioner [26].
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33
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33750349260
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note
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For example, the relativistic perturbations of the ray trajectory caused by the time-dependent quadrupole moment of a self-gravitating body at rest have been analyzed in [7].
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34
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85107715453
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note
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3) are Cartesian coordinates in three-dimensional Euclidean space.
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35
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33750288073
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note
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Throughout this paper, we use units such that Newton's gravitational constant G and the speed of light c equal unity.
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36
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33750288612
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note
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Greek indices run from 0 to 3 and Latin indices from 1 to 3. Repeated indices assume the Einstein summation rule. Bold letters denote three-dimensional Euclidean vectors.
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38
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0002876543
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Isolated Gravitating System in General Relativity, "Enrico Fermi," edited by J. Ehlers (North-Holland, Amsterdam)
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W.G. Dixon, in Isolated Gravitating System in General Relativity, Proceedings of the International School of Physics "Enrico Fermi," edited by J. Ehlers (North-Holland, Amsterdam, 1979), p. 156.
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Dixon, W.G.1
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42
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85107714904
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note
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123= +1.
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44
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33750317022
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note
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Equation (12) evidently implies that gravity propagates with the speed of light c= 1 in the first post-Minkowskian approximation.
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45
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85107714792
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note
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β=0, where a comma denotes partial differentiation.
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46
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33750369449
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note
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See, for example, the textbooks [47] and [50], the classical review [49], and references therein. Derivation and proofs of equations of the present section are also given in Appendix A.
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51
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33750370526
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note
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The tetrad indices run from 0 to 3 and indicate time and space coordinates. The indices enclosed in parentheses indicate the different vectors of the tetrad and also run from 0 to 3. It is worth noting that the time-space indices of the tetrad have no relation to the other tetrad indices. If one changes the space-time coordinates then each tetrad vector changes in accordance with the transformation law for vectors. On the other hand, one can change the basis vectors at each point in space-time by a Lorentz transformation without changing the coordinate chart [52].
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54
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33750289174
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note
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The distance X is usually much smaller than the distance between the pulsar and its companion and is about 5-10 times the radius of a neutron star.
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65
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0001536266
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G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A.G. Mann, S. Chang, A.N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
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Laurent, Ph.2
Lemonde, P.3
Clairon, A.4
Mann, A.G.5
Chang, S.6
Luiten, A.N.7
Salomon, C.8
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66
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0040645775
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A. Spallicci, A. Brillet, G. Busca, G. Catastini, I. Pinto, I. Roxburgh, C. Salomon, M. Soffel, and C. Veillet, Class. Quantum Grav. 14, 2971 (1997).
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0008400697
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edited by C. Lämmerzahl, C.W.F. Everitt, and F.W. Hehl (Springer-Verlag, Berlin)
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L. Blanchet, S.M. Kopeikin, and G. Schäfer, in Gyros, Clocks, and Interferometers: Testing Relativistic Gravity in Space, edited by C. Lämmerzahl, C.W.F. Everitt, and F.W. Hehl (Springer-Verlag, Berlin, 2001), pp. 141-166.
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Blanchet, L.1
Kopeikin, S.M.2
Schäfer, G.3
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77
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33750316478
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note
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gr of the gravitational wave.
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79
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33750336383
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note
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Braginsky et al. [80] also probably knew this result as it follows from one of the footnotes in their paper. However, they did not give a precise mathematical proof of that fact.
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80
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0000672401
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in Russian
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V.B. Braginsky, L.P. Grishchuk, A.G. Doroshkevich, Ya.B. Zeldovich, I.D. Novikov and M.V. Sazhin, Zh. Eksp. Teor. Fiz. 65, 1729 (1974) (in Russian).
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Braginsky, V.B.1
Grishchuk, L.P.2
Doroshkevich, A.G.3
Zeldovich, Y.B.4
Novikov, I.D.5
Sazhin, M.V.6
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83
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0003952210
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Report No. MPQ 233
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"LISA Pre-Phase: A Report," Report No. MPQ 233, 1998, ftp://ftp.ipp-garching.mpg.de/pub/grav/lisa/ppa2.05.ps.gz
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0033587303
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A. Melchiorri, M.V. Sazhin, V.V. Shulga, and N. Vittorio, Astrophys. J. 518, 562 (1999).
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89
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85107712260
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note
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α. This is due to the complete antisymmetry of the equation with respect to the cyclic permutation of all indices.
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