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Gravitational radiation from post-Newtonian sources and inspiralling compact binaries. (English) Zbl 1316.83003

Summary: To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries – binary star systems composed of neutron stars and/or black holes in their late stage of evolution – require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries – moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.
Update to the author’s paper [Zbl 1023.83001], see also update [Zbl 1316.83004]: Major revision, updated and expanded. About 180 new references.

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C35 Gravitational waves
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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References:

[1] Abbott, B. P. et al. (LIGO Scientific Collaboration and Virgo Collaboration), “Observation of Gravitational Waves from a Binary Black Hole Merger”, Phys. Rev. Lett., 116, 061102 (2016). [DOI], [ADS], [arXiv:1602.03837 [gr-qc]]. (Cited on page 7.) · doi:10.1103/PhysRevLett.116.061102
[2] Abramowicz, M. A. and Kluźniak, W., “A precise determination of black hole spin in GRO J1655-40”, Astron. Astrophys., 374, L19-L20 (2001). [DOI], [ADS], [astro-ph/0105077]. (Cited on page 146.) · doi:10.1051/0004-6361:20010791
[3] Ajith, P., Iyer, B. R., Robinson, C. A. K. and Sathyaprakash, B. S., “New class of post-Newtonian approximants to the waveform templates of inspiralling compact binaries: Test mass in the Schwarzschild spacetime”, Phys. Rev. D, 71, 044029 (2005). [gr-qc/0412033]. (Cited on pages 65 and 131.) · doi:10.1103/PhysRevD.71.044029
[4] Ajith, P. et al., “Template bank for gravitational waveforms from coalescing binary black holes: Nonspinning binaries”, Phys. Rev. D, 77, 104017 (2008). [DOI], [ADS], [arXiv:0710.2335 [gr-qc]]. Erratum: Phys. Rev. D, 79, 129901(E) (2009). (Cited on page 65.) · doi:10.1103/PhysRevD.77.104017
[5] Alvi, K., “Energy and angular momentum flow into a black hole in a binary”, Phys. Rev. D, 64, 104020 (2001). [DOI], [arXiv:0107080 [gr-qc]]. (Cited on page 158.) · doi:10.1103/PhysRevD.64.104020
[6] Anderson, J. L. and DeCanio, T. C., “Equations of hydrodynamics in general relativity in the slow motion approximation”, Gen. Relativ. Gravit., 6, 197-237 (1975). [DOI]. (Cited on pages 53, 57, and 58.) · Zbl 0379.76101 · doi:10.1007/BF00769986
[7] Anderson, J. L., Kates, R. E., Kegeles, L. S. and Madonna, R. G., “Divergent integrals of post-Newtonian gravity: Nonanalytic terms in the near-zone expansion of a gravitationally radiating system found by matching”, Phys. Rev. D, 25, 2038-2048 (1982). [DOI], [ADS]. (Cited on pages 11, 44, and 46.) · doi:10.1103/PhysRevD.25.2038
[8] Apostolatos, T. A., Cutler, C., Sussman, G. J. and Thorne, K. S., “Spin induced orbital precession and its modulation of the gravitational wave forms from merging binaries”, Phys. Rev. D, 49, 6274-6297 (1994). [DOI]. (Cited on pages 21 and 146.) · doi:10.1103/PhysRevD.49.6274
[9] Arun, K. G., Blanchet, L., Iyer, B. R. and Qusailah, M. S., “Inspiralling compact binaries in quasi-elliptical orbits: The complete 3PN energy flux”, Phys. Rev. D, 77, 064035 (2008). [DOI], [arXiv:0711.0302]. (Cited on pages 20, 92, 138, 140, 141, and 142.) · doi:10.1103/PhysRevD.77.064035
[10] Arun, K. G., Blanchet, L., Iyer, B. R. and Qusailah, M. S., “Tail effects in the 3PN gravitational wave energy flux of compact binaries in quasi-elliptical orbits”, Phys. Rev. D, 77, 064034 (2008). [DOI], [arXiv:0711.0250]. (Cited on pages 20, 141, 143, and 144.) · doi:10.1103/PhysRevD.77.064034
[11] Arun, K. G., Blanchet, L., Iyer, B. R. and Qusailah, M. S. S., “The 2.5PN gravitational wave polarizations from inspiralling compact binaries in circular orbits”, Class. Quantum Grav., 21, 3771-3801 (2004). [DOI], [gr-qc/0404185]. Erratum: Class. Quantum Grav., 22, 3115 (2005). (Cited on pages 20, 21, 117, 125, 126, and 130.) · Zbl 1075.83015 · doi:10.1088/0264-9381/21/15/010
[12] Arun, K. G., Blanchet, L., Iyer, B. R. and Sinha, S., “Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits”, Phys. Rev. D, 80, 124018 (2009). [DOI], [arXiv:0908.3854]. (Cited on pages 20, 141, and 145.) · doi:10.1103/PhysRevD.80.124018
[13] Arun, K. G., Buonanno, A., Faye, G. and Ochsner, E., “Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms”, Phys. Rev. D, 79, 104023 (2009). [DOI], [arXiv:0810.5336]. (Cited on page 155.) · doi:10.1103/PhysRevD.79.104023
[14] Arun, K. G., Iyer, B. R., Qusailah, M. S. S. and Sathyaprakash, B. S., “Probing the non-linear structure of general relativity with black hole binaries”, Phys. Rev. D, 74, 024006 (2006). [DOI], [gr-qc/0604067]. (Cited on pages 16 and 131.) · doi:10.1103/PhysRevD.74.024006
[15] Arun, K. G., Iyer, B. R., Qusailah, M. S. S. and Sathyaprakash, B. S., “Testing post-Newtonian theory with gravitational wave observations”, Class. Quantum Grav., 23, L37-L43 (2006). [DOI], [ADS], [arXiv:gr-qc/0604018]. (Cited on pages 16 and 131.) · Zbl 1101.83302 · doi:10.1088/0264-9381/23/9/L01
[16] Arun, K. G., Iyer, B. R., Sathyaprakash, B. S. and Sinha, S., “Higher harmonics increase LISA’s mass reach for supermassive black holes”, Phys. Rev. D, 75, 124002 (2007). [DOI], [arXiv:0704.1086]. (Cited on page 20.) · doi:10.1103/PhysRevD.75.124002
[17] Arun, K. G., Iyer, B. R., Sathyaprakash, B. S., Sinha, S. and Van Den Broeck, C., “Higher signal harmonics, LISA’s angular resolution, and dark energy”, Phys. Rev. D, 76, 104016 (2007). [DOI], [ADS], [arXiv:0707.3920]. (Cited on page 20.) · doi:10.1103/PhysRevD.76.104016
[18] Arun, K. G., Iyer, B. R., Sathyaprakash, B. S. and Sundararajan, P. A., “Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case”, Phys. Rev. D, 71, 084008 (2005). [DOI], [gr-qc/0411146]. (Cited on pages 65 and 131.) · doi:10.1103/PhysRevD.71.084008
[19] Bailey, I. and Israel, W., “Lagrangian dynamics of spinning particles and polarized media in general relativity”, Commun. Math. Phys., 42, 65 (1975). [DOI]. (Cited on pages 148 and 149.) · doi:10.1007/BF01609434
[20] Baker, J. G., Centrella, J., Choi, D.-I., Koppitz, M., van Meter, J. and Miller, M. C., “Getting a kick out of numerical relativity”, Astrophys. J., 653, L93-L96 (2006). [DOI], [astro-ph/0603204]. (Cited on page 22.) · Zbl 1202.70060 · doi:10.1086/510448
[21] Baker, J. G., Centrella, J., Choi, D.-I., Koppitz, M. and van Meter, J. R., “Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes”, Phys. Rev. Lett., 96, 111102 (2006). [DOI], [ADS], [arXiv:gr-qc/0511103]. (Cited on page 8.) · doi:10.1103/PhysRevLett.96.111102
[22] Barack, L., “Gravitational self-force in extreme mass-ratio inspirals”, Class. Quantum Grav., 26, 213001 (2009). [DOI], [ADS], [arXiv:0908.1664 [gr-qc]]. (Cited on page 112.) · Zbl 1180.83001 · doi:10.1088/0264-9381/26/21/213001
[23] Barack, L.; Blanchet, L. (ed.); Spallicci, A. (ed.); Whiting, B. (ed.), Computational Methods for the Self-Force in Black Hole Spacetimes, Lectures from the CNRS School on Mass, Orléans, France, 23-25 June 2008, Dordrecht; New York · Zbl 1213.83032
[24] Barack, L. and Sago, N., “Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole”, Phys. Rev. Lett., 102, 191101 (2009). [DOI], [arXiv:0902.0573]. (Cited on page 108.) · doi:10.1103/PhysRevLett.102.191101
[25] Barausse, E., Racine, E. and Buonanno, A., “Hamiltonian of a spinning test particle in curved spacetime”, Phys. Rev. D, 80, 104025 (2009). [DOI], [arXiv:0907.4745 [gr-qc]]. (Cited on page 148.) · doi:10.1103/PhysRevD.80.104025
[26] Bardeen, J. M., Carter, B. and Hawking, S. W., “The Four Laws of Black Hole Mechanics”, Commun. Math. Phys., 31, 161-170 (1973). [DOI], [ADS]. (Cited on page 110.) · Zbl 1125.83309 · doi:10.1007/BF01645742
[27] Barker, B. M. and O’Connell, R. F., “Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments”, Phys. Rev. D, 12, 329-335 (1975). [DOI]. (Cited on pages 19, 102, and 147.) · doi:10.1103/PhysRevD.12.329
[28] Barker, B. M. and O’Connell, R. F., “The Gravitational Interaction: Spin, Rotation, and Quantum Effects — A Review”, Gen. Relativ. Gravit., 11, 149-175 (1979). [DOI]. (Cited on pages 19, 102, and 147.) · doi:10.1007/BF00756587
[29] Baumgarte, T. W., “Innermost stable circular orbit of binary black holes”, Phys. Rev. D, 62, 024018 (2000). [DOI], [ADS]. (Cited on page 103.) · doi:10.1103/PhysRevD.62.024018
[30] Bekenstein, J. D., “Gravitational Radiation Recoil and Runaway Black Holes”, Astrophys. J., 183, 657-664 (1973). [DOI], [ADS]. (Cited on pages 10 and 22.) · doi:10.1086/152255
[31] Bel, L., Damour, T., Deruelle, N., Ibáñez, J. and Martin, J., “Poincaré-Invariant Gravitational Field and Equations of Motion of two Pointlike Objects: The Postlinear Approximation of General Relativity”, Gen. Relativ. Gravit., 13, 963-1004 (1981). [DOI]. (Cited on page 17.) · doi:10.1007/BF00756073
[32] Benacquista, M. J. and Downing, J. M. B., “Relativistic Binaries in Globular Clusters”, Living Rev. Relativity, 16, lrr-2013-4 (2013). [DOI], [ADS], [arXiv:1110.4423]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2013-4. (Cited on page 135.) · Zbl 1316.85006
[33] Bernard, L., Blanchet, L., Bohé, A., Faye, G. and Marsat, S., “Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation”, arXiv, e-print, (2015). [arXiv:1512.02876 [gr-qc]]. (Cited on page 19.)
[34] Berti, E., Cardoso, V., Gonzalez, J. A., Sperhake, U., Hannam, M., Husa, S. and Brügmann, B., “Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis”, Phys. Rev. D, 76, 064034 (2007). [DOI], [ADS], [arXiv:gr-qc/0703053]. (Cited on page 36.) · doi:10.1103/PhysRevD.76.064034
[35] Bertotti, B. and Plebański, J. F., “Theory of gravitational perturbations in the fast motion approximation”, Ann. Phys. (N.Y.), 11, 169-200 (1960). [DOI]. (Cited on page 18.) · Zbl 0094.23102 · doi:10.1016/0003-4916(60)90132-9
[36] Bini, D. and Damour, T., “Analytical determination of the two-body gravitational interaction potential at the fourth post-Newtonian approximation”, Phys. Rev. D, 87, 121501 (2013). [DOI], [ADS], [arXiv:1305.4884 [gr-qc]]. (Cited on pages 19, 96, and 114.) · doi:10.1103/PhysRevD.87.121501
[37] Bini, D. and Damour, T., “Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential”, Phys. Rev. D, 89, 104047 (2014). [DOI], [arXiv:1403.2366 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.89.104047
[38] Bini, D. and Damour, T., “High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations”, Phys. Rev. D, 89, 064063 (2014). [DOI], [arXiv:1312.2503 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.89.064063
[39] Bini, D., Damour, T. and Geralico, A., “Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole”, arXiv, e-print, (2015). [arXiv:1511.04533 [gr-qc]]. (Cited on page 19.)
[40] Blaes, O., Lee, M. H. and Socrates, A., “The Kozai Mechanism and the Evolution of Binary Super-massive Black Holes”, Astrophys. J., 578, 775-786 (2002). [DOI], [ADS], [astro-ph/0203370]. (Cited on page 135.) · doi:10.1086/342655
[41] Blanchet, L., “Radiative gravitational fields in general-relativity. II. Asymptotic-behaviour at future null infinity”, Proc. R. Soc. London, Ser. A, 409, 383-399 (1987). [DOI]. (Cited on pages 10, 11, 33, and 35.) · Zbl 0658.35084 · doi:10.1098/rspa.1987.0022
[42] Blanchet, L., Contribution à l’étude du rayonnement gravitationnel émis par un système isolé, Habil. thesis, (Universitré Paris VI, Paris, 1990). (Cited on pages 21 and 43.)
[43] Blanchet, L., “Time asymmetric structure of gravitational radiation”, Phys. Rev. D, 47, 4392-4420 (1993). [DOI]. (Cited on pages 11, 18, 19, 46, 57, 58, 63, and 117.) · doi:10.1103/PhysRevD.47.4392
[44] Blanchet, L., “Second-post-Newtonian generation of gravitational radiation”, Phys. Rev. D, 51, 2559-2583 (1995). [DOI], [gr-qc/9501030]. (Cited on pages 11, 12, 20, 37, 46, 48, 51, and 64.) · doi:10.1103/PhysRevD.51.2559
[45] Blanchet, L., “Energy losses by gravitational radiation in inspiralling compact binaries to five halves post-Newtonian order”, Phys. Rev. D, 54, 1417-1438 (1996). [DOI], [gr-qc/9603048]. Erratum: Phys. Rev. D, 71, 129904(E) (2005). (Cited on pages 20 and 91.) · doi:10.1103/PhysRevD.54.1417
[46] Blanchet, L.; Marck, J-A (ed.); Lasota, J-P (ed.), Gravitational radiation from relativistic sources, Proceedings of the Les Houches School of Physics, Les Houches, Haute Savoie, 26 September-6 October, 1995, Cambridge
[47] Blanchet, L., “Gravitational radiation reaction and balance equations to post-Newtonian order”, Phys. Rev. D, 55, 714-732 (1997). [DOI], [gr-qc/9609049]. (Cited on pages 11, 18, 63, 64, and 117.) · doi:10.1103/PhysRevD.55.714
[48] Blanchet, L., “Gravitational-wave tails of tails”, Class. Quantum Grav., 15, 113-141 (1998). [DOI], [gr-qc/9710038]. Erratum: Class. Quantum Grav., 22, 3381 (2005). (Cited on pages 11, 20, 39, 40, 43, and 44.) · Zbl 0925.53027 · doi:10.1088/0264-9381/15/1/009
[49] Blanchet, L., “On the multipole expansion of the gravitational field”, Class. Quantum Grav., 15, 1971-1999 (1998). [DOI], [gr-qc/9801101]. (Cited on pages 11, 12, 46, 48, and 51.) · Zbl 0937.83008 · doi:10.1088/0264-9381/15/7/013
[50] Blanchet, L., “Quadrupole-quadrupole gravitational waves”, Class. Quantum Grav., 15, 89-111 (1998). [DOI], [gr-qc/9710037]. (Cited on pages 11, 21, 39, and 43.) · Zbl 0925.53030 · doi:10.1088/0264-9381/15/1/008
[51] Blanchet, L., “Innermost circular orbit of binary black holes at the third post-Newtonian approximation”, Phys. Rev. D, 65, 124009 (2002). [DOI], [gr-qc/0112056]. (Cited on pages 101, 103, and 110.) · doi:10.1103/PhysRevD.65.124009
[52] Blanchet, L.; Blanchet, L. (ed.); Spallicci, A. (ed.); Whiting, B. (ed.), Post-Newtonian theory and the two-body problem, Lectures from the CNRS School on Mass, Orléans, France, 23-25 June 2008, Dordrecht; New York · Zbl 1209.83003 · doi:10.1007/978-90-481-3015-3
[53] Blanchet, L., Buonanno, A. and Faye, G., “Higher-order spin effects in the dynamics of compact binaries II. Radiation field”, Phys. Rev. D, 74, 104034 (2006). [DOI], [gr-qc/0605140]. Erratum: Phys. Rev. D, 75, 049903 (2007). (Cited on pages 21, 147, and 158.) · doi:10.1103/PhysRevD.74.104034
[54] Blanchet, L., Buonanno, A. and Faye, G., “Tail-induced spin-orbit effect in the gravitational radiation of compact binaries”, Phys. Rev. D, 84, 064041 (2011). [DOI], [arXiv:1104.5659 [gr-qc]]. (Cited on pages 21, 147, 154, 158, and 159.) · doi:10.1103/PhysRevD.84.064041
[55] Blanchet, L., Buonanno, A. and Le Tiec, A., “First law of mechanics for black hole binaries with spins”, Phys. Rev. D, 87, 024030 (2013). [DOI], [arXiv:1211.1060 [gr-qc]]. (Cited on pages 102, 103, and 111.) · doi:10.1103/PhysRevD.87.024030
[56] Blanchet, L. and Damour, T., “Multipolar radiation reaction in general relativity”, Phys. Lett. A, 104, 82-86 (1984). [DOI]. (Cited on page 63.) · doi:10.1016/0375-9601(84)90967-8
[57] Blanchet, L. and Damour, T., “Radiative gravitational fields in general relativity I. General structure of the field outside the source”, Philos. Trans. R. Soc. London, Ser. A, 320, 379-430 (1986). [DOI]. (Cited on pages 10, 11, 20, 26, 27, 29, 31, and 33.) · Zbl 0604.35073 · doi:10.1098/rsta.1986.0125
[58] Blanchet, L. and Damour, T., “Tail-transported temporal correlations in the dynamics of a gravitating system”, Phys. Rev. D, 37, 1410-1435 (1988). [DOI]. (Cited on pages 11, 19, 43, 44, 46, 57, 58, 59, and 63.) · doi:10.1103/PhysRevD.37.1410
[59] Blanchet, L. and Damour, T., “Post-Newtonian generation of gravitational waves”, Ann. Inst. Henri Poincare A, 50, 377-408 (1989). (Cited on pages 11, 37, 46, and 49.) · Zbl 0684.53059
[60] Blanchet, L. and Damour, T., “Hereditary effects in gravitational radiation”, Phys. Rev. D, 46, 4304-4319 (1992). [DOI]. (Cited on pages 11, 20, 21, 39, 43, 57, and 122.) · doi:10.1103/PhysRevD.46.4304
[61] Blanchet, L., Damour, T. and Esposito-Farèse, G., “Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates”, Phys. Rev. D, 69, 124007 (2004). [DOI], [gr-qc/0311052]. (Cited on pages 18, 70, 72, 74, and 75.) · doi:10.1103/PhysRevD.69.124007
[62] Blanchet, L., Damour, T., Esposito-Farèse, G. and Iyer, B. R., “Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order”, Phys. Rev. Lett., 93, 091101 (2004). [DOI], [gr-qc/0406012]. (Cited on pages 20, 71, 77, 78, and 117.) · doi:10.1103/PhysRevLett.93.091101
[63] Blanchet, L., Damour, T., Esposito-Farèse, G. and Iyer, B. R., “Dimensional regularization of the third post-Newtonian gravitational wave generation of two point masses”, Phys. Rev. D, 71, 124004 (2005). [DOI], [ADS], [gr-qc/0503044]. (Cited on pages 20, 71, 77, 78, and 117.) · doi:10.1103/PhysRevD.71.124004
[64] Blanchet, L., Damour, T. and Iyer, B. R., “Gravitational waves from inspiralling compact binaries: Energy loss and wave form to second post-Newtonian order”, Phys. Rev. D, 51, 5360-5386 (1995). [DOI], [gr-qc/9501029]. (Cited on pages 20, 97, and 117.) · doi:10.1103/PhysRevD.51.5360
[65] Blanchet, L., Damour, T. and Iyer, B. R., “Surface-integral expressions for the multipole moments of post-Newtonian sources and the boosted Schwarzschild solution”, Class. Quantum Grav., 22, 155 (2005). [DOI], [gr-qc/0410021]. (Cited on pages 53 and 71.) · Zbl 1060.83031 · doi:10.1088/0264-9381/22/1/011
[66] Blanchet, L., Damour, T., Iyer, B. R., Will, C. M. and Wiseman, A. G., “Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian Order”, Phys. Rev. Lett., 74, 3515-3518 (1995). [DOI], [gr-qc/9501027]. (Cited on page 20.) · doi:10.1103/PhysRevLett.74.3515
[67] Blanchet, L., Detweiler, S., Le Tiec, A. and Whiting, B. F., “Higher-order Post-Newtonian fit of the gravitational self-force for circular orbits in the Schwarzschild geometry”, Phys. Rev. D, 81, 084033 (2010). [DOI], [ADS], [arXiv:1002.0726 [gr-qc]]. (Cited on pages 95, 112, 113, 114, and 115.) · doi:10.1103/PhysRevD.81.084033
[68] Blanchet, L., Detweiler, S., Le Tiec, A. and Whiting, B. F., “Post-Newtonian and numerical calculations of the gravitational self-force for circular orbits in the Schwarzschild geometry”, Phys. Rev. D, 81, 064004 (2010). [DOI], [ADS], [arXiv:0910.0207 [gr-qc]]. (Cited on pages 60, 112, 113, 114, and 115.) · doi:10.1103/PhysRevD.81.064004
[69] Blanchet, L. and Faye, G., “Equations of motion of point-particle binaries at the third post-Newtonian order”, Phys. Lett. A, 271, 58-64 (2000). [DOI], [gr-qc/0004009]. (Cited on pages 17, 68, 69, 70, 71, 74, 77, 82, and 95.) · Zbl 1223.83020 · doi:10.1016/S0375-9601(00)00360-1
[70] Blanchet, L. and Faye, G., “Hadamard regularization”, J. Math. Phys., 41, 7675-7714 (2000). [DOI], [gr-qc/0004008]. (Cited on pages 17, 66, 67, 68, 69, 74, and 75.) · Zbl 0986.46024 · doi:10.1063/1.1308506
[71] Blanchet, L. and Faye, G., “General relativistic dynamics of compact binaries at the third post-Newtonian order”, Phys. Rev. D, 63, 062005 (2001). [DOI], [gr-qc/0007051]. (Cited on pages 17, 24, 59, 68, 69, 70, 71, 74, 76, 77, and 82.) · doi:10.1103/PhysRevD.63.062005
[72] Blanchet, L. and Faye, G., “Lorentzian regularization and the problem of point-like particles in general relativity”, J. Math. Phys., 42, 4391-4418 (2001). [DOI], [gr-qc/0006100]. (Cited on pages 17, 66, 68, 69, and 75.) · Zbl 1009.83007 · doi:10.1063/1.1384864
[73] Blanchet, L., Faye, G., Iyer, B. R. and Joguet, B., “Gravitational-wave inspiral of compact binary systems to 7/2 post-Newtonian order”, Phys. Rev. D, 65, 061501(R) (2002). [DOI], [gr-qc/0105099]. Erratum: Phys. Rev. D, 71, 129902(E) (2005). (Cited on pages 20 and 71.) · doi:10.1103/PhysRevD.65.061501
[74] Blanchet, L., Faye, G., Iyer, B. R. and Sinha, S., “The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits”, Class. Quantum Grav., 25, 165003 (2008). [DOI], [arXiv:0802.1249]. (Cited on pages 11, 20, 31, 40, 44, 117, 118, 119, 125, and 132.) · Zbl 1147.83300 · doi:10.1088/0264-9381/25/16/165003
[75] Blanchet, L., Faye, G. and Nissanke, S., “Structure of the post-Newtonian expansion in general relativity”, Phys. Rev. D, 72, 044024 (2005). [DOI]. (Cited on pages 11, 54, 58, and 59.) · doi:10.1103/PhysRevD.72.044024
[76] Blanchet, L., Faye, G. and Ponsot, B., “Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order”, Phys. Rev. D, 58, 124002 (1998). [DOI], [gr-qc/9804079]. (Cited on pages 17, 68, 78, 97, and 112.) · doi:10.1103/PhysRevD.58.124002
[77] Blanchet, L., Faye, G. and Whiting, B. F., “Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries”, Phys. Rev. D, 89, 064026 (2014). [DOI], [arXiv:1312.2975 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.89.064026
[78] Blanchet, L., Faye, G. and Whiting, B. F., “High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries”, Phys. Rev. D, 90, 044017 (2014). [DOI], [arXiv:1405.5151 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.90.044017
[79] Blanchet, L. and Iyer, B. R., “Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame”, Class. Quantum Grav., 20, 755 (2003). [DOI], [gr-qc/0209089]. (Cited on pages 17, 90, 91, 94, 103, and 135.) · Zbl 1028.83013 · doi:10.1088/0264-9381/20/4/309
[80] Blanchet, L. and Iyer, B. R., “Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses”, Phys. Rev. D, 71, 024004 (2005). [DOI], [gr-qc/0409094]. (Cited on pages 20, 71, 76, 77, 78, and 117.) · doi:10.1103/PhysRevD.71.024004
[81] Blanchet, L., Iyer, B. R. and Joguet, B., “Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order”, Phys. Rev. D, 65, 064005 (2002). [gr-qc/0105098]. Erratum: Phys. Rev. D, 71, 129903(E) (2005). (Cited on pages 20, 71, 76, 77, 78, 117, 118, 119, and 145.) · doi:10.1103/PhysRevD.65.064005
[82] Blanchet, L., Iyer, B. R., Will, C. M. and Wiseman, A. G., “Gravitational wave forms from in-spiralling compact binaries to second-post-Newtonian order”, Class. Quantum Grav., 13, 575-584 (1996). [DOI], [gr-qc/9602024]. (Cited on pages 20 and 125.) · Zbl 0875.53011 · doi:10.1088/0264-9381/13/4/002
[83] Blanchet, L., Qusailah, M. S. and Will, C. M., “Gravitational recoil of inspiraling black-hole binaries to second post-Newtonian order”, Astrophys. J., 635, 508 (2005). [DOI], [astro-ph/0507692]. (Cited on page 22.) · doi:10.1086/497332
[84] Blanchet, L. and Sathyaprakash, B. S., “Signal analysis of gravitational wave tails”, Class. Quantum Grav., 11, 2807-2831 (1994). [DOI]. (Cited on pages 16 and 131.) · doi:10.1088/0264-9381/11/11/020
[85] Blanchet, L. and Sathyaprakash, B. S., “Detecting a Tail Effect in Gravitational-Wave Experiments”, Phys. Rev. Lett., 74, 1067-1070 (1995). [DOI], [ADS]. (Cited on pages 16 and 131.) · doi:10.1103/PhysRevLett.74.1067
[86] Blanchet, L. and Schafer, G., “Higher order gravitational radiation losses in binary systems”, Mon. Not. R. Astron. Soc., 239, 845-867 (1989). [DOI]. (Cited on pages 20, 117, 140, and 145.) · Zbl 0671.70009 · doi:10.1093/mnras/239.3.845
[87] Blanchet, L. and Schäfer, G., “Gravitational wave tails and binary star systems”, Class. Quantum Grav., 10, 2699-2721 (1993). [DOI]. (Cited on pages 14, 20, 122, 126, 140, 144, and 145.) · doi:10.1088/0264-9381/10/12/026
[88] Bohé, A., Faye, G., Marsat, S. and Porter, E. K., “Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order”, Class. Quantum Grav., 32, 195010 (2015). [DOI], [arXiv:1501.01529 [gr-qc]]. (Cited on pages 21 and 147.) · Zbl 1327.83097 · doi:10.1088/0264-9381/32/19/195010
[89] Bohé, A., Marsat, S. and Blanchet, L., “Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries”, Class. Quantum Grav., 30, 135009 (2013). [arXiv:1303.7412]. (Cited on pages 21, 147, 158, and 159.) · Zbl 1273.83050 · doi:10.1088/0264-9381/30/13/135009
[90] Bohé, A., Marsat, S., Faye, G. and Blanchet, L., “Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binary systems”, Class. Quantum Grav., 30, 075017 (2013). [arXiv:1212.5520]. (Cited on pages 19, 147, 151, 153, 154, 156, and 158.) · Zbl 1266.83035 · doi:10.1088/0264-9381/30/7/075017
[91] Bollini, C. G. and Giambiagi, J. J., “Lowest order ‘divergent’ graphs in <Emphasis Type=”Italic“>v-dimensional space”, Phys. Lett. B, 40, 566-568 (1972). [DOI]. (Cited on page 72.) · doi:10.1016/0370-2693(72)90483-2
[92] Bonazzola, S., Gourgoulhon, E. and Marck, J.-A., “Numerical models of irrotational binary neutron stars in general relativity”, Phys. Rev. Lett., 82, 892-895 (1999). [DOI], [ADS], [arXiv:gr-qc/9810072 [gr-qc]]. (Cited on page 101.) · Zbl 0961.85002 · doi:10.1103/PhysRevLett.82.892
[93] Bondi, H., van der Burg, M. G. J. and Metzner, A. W. K., “Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems”, Proc. R. Soc. London, Ser. A, 269, 21-52 (1962). [DOI], [ADS]. (Cited on pages 10, 11, 33, and 41.) · Zbl 0106.41903 · doi:10.1098/rspa.1962.0161
[94] Bonnor, W. B., “Spherical gravitational waves”, Philos. Trans. R. Soc. London, Ser. A, 251, 233-271 (1959). [DOI]. (Cited on pages 10 and 26.) · Zbl 0084.43906 · doi:10.1098/rsta.1959.0003
[95] Bonnor, W. B. and Rotenberg, M. A., “Transport of momentum by gravitational waves: Linear approximation”, Proc. R. Soc. London, Ser. A, 265, 109-116 (1961). [DOI]. (Cited on pages 10 and 26.) · Zbl 0100.40506 · doi:10.1098/rspa.1961.0226
[96] Bonnor, W. B. and Rotenberg, M. A., “Gravitational waves from isolated sources”, Proc. R. Soc. London, Ser. A, 289, 247-274 (1966). [DOI]. (Cited on pages 10 and 26.) · doi:10.1098/rspa.1966.0010
[97] Boyle, M., Brown, D. A., Kidder, L. E., Mroué, A. H., Pfeiffer, H. P., Scheel, M. A., Cook, G. B. and Teukolsky, S. A., “High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions”, Phys. Rev. D, 76, 124038 (2007). [DOI], [ADS], [arXiv:0710.0158 [gr-qc]]. (Cited on page 36.) · doi:10.1103/PhysRevD.76.124038
[98] Boyle, M., Buonanno, A., Kidder, L. E., Mroué, A. H., Pan, Y., Pfeiffer, H. P. and Scheel, M. A., “High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants”, Phys. Rev. D, 78, 104020 (2008). [DOI], [arXiv:0804.4184 [gr-qc]]. (Cited on pages 36 and 124.) · doi:10.1103/PhysRevD.78.104020
[99] Braginsky, V. B. and Thorne, K. S., “Gravitational-wave bursts with memory and experimental prospects”, Nature, 327, 123-125 (1987). [DOI]. (Cited on page 21.) · doi:10.1038/327123a0
[100] Breitenlohner, P. and Maison, D., “Dimensional renormalization and the action principle”, Commun. Math. Phys., 52, 11-38 (1977). [DOI]. (Cited on page 72.) · doi:10.1007/BF01609069
[101] Brenneman, L. W. and Reynolds, C. S., “Constraining Black Hole Spin via X-Ray Spectroscopy”, Astrophys. J., 652, 1028-1043 (2006). [DOI], [ADS], [arXiv:astro-ph/0608502]. (Cited on page 146.) · doi:10.1086/508146
[102] Brenneman, L. W. et al., “The Spin of the Supermassive Black Hole in NGC 3783”, Astrophys. J., 736, 103 (2011). [DOI], [arXiv:1104.1172 [astro-ph.HE]]. (Cited on page 146.) · doi:10.1088/0004-637X/736/2/103
[103] Breuer, R. and Rudolph, E., “Radiation reaction and energy loss in the post-Newtonian approximation of general relativity”, Gen. Relativ. Gravit., 13, 777 (1981). [DOI]. (Cited on page 13.) · doi:10.1007/BF00758216
[104] Bruhat, Y.; Witten, L. (ed.), The Cauchy Problem, 130-168 (1962), New York; London
[105] Buonanno, A., Chen, Y. and Vallisneri, M., “Detection template families for gravitational waves from the final stages of binary black-holes binaries: Nonspinning case”, Phys. Rev. D, 67, 024016 (2003). [DOI], [gr-qc/0205122]. (Cited on pages 65, 71, 125, and 131.) · doi:10.1103/PhysRevD.67.024016
[106] Buonanno, A., Chen, Y. and Vallisneri, M., “Detection template families for precessing binaries of spinning compact binaries: Adiabatic limit”, Phys. Rev. D, 67, 104025 (2003). [DOI], [gr-qc/0211087]. (Cited on pages 65, 71, 125, and 131.) · doi:10.1103/PhysRevD.67.104025
[107] Buonanno, A., Cook, G. B. and Pretorius, F., “Inspiral, merger, and ring-down of equal-mass blackhole binaries”, Phys. Rev. D, 75, 124018 (2007). [DOI], [ADS], [gr-qc/0610122]. (Cited on page 36.) · doi:10.1103/PhysRevD.75.124018
[108] Buonanno, A. and Damour, T., “Effective one-body approach to general relativistic two-body dynamics”, Phys. Rev. D, 59, 084006 (1999). [DOI], [ADS], [arXiv:gr-qc/9811091]. (Cited on page 65.) · doi:10.1103/PhysRevD.59.084006
[109] Buonanno, A. and Damour, T., “Transition from inspiral to plunge in binary black hole coalescences”, Phys. Rev. D, 62, 064015 (2000). [DOI], [ADS], [arXiv:gr-qc/0001013]. (Cited on page 65.) · doi:10.1103/PhysRevD.62.064015
[110] Buonanno, A., Faye, G. and Hinderer, T., “Spin effects on gravitational waves from inspiralling compact binaries at second post-Newtonian order”, Phys. Rev. D, 87, 044009 (2013). [DOI], [arXiv:1209.6349]. (Cited on page 147.) · doi:10.1103/PhysRevD.87.044009
[111] Buonanno, A., Iyer, B. R., Pan, Y., Ochsner, E. and Sathyaprakash, B. S., “Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors”, Phys. Rev. D, 80, 084043 (2009). [DOI], [arXiv:0907.0700 [gr-qc]]. (Cited on pages 65 and 131.) · doi:10.1103/PhysRevD.80.084043
[112] Buonanno, A., Pan, Y., Pfeiffer, H. P., Scheel, M. A., Buchman, L. T. and Kidder, L. E., “Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonspinning, equal-mass black holes”, Phys. Rev. D, 79, 124028 (2009). [DOI], [ADS], [arXiv:0902.0790 [gr-qc]]. (Cited on page 65.) · doi:10.1103/PhysRevD.79.124028
[113] Burke, W. L., “Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions”, J. Math. Phys., 12, 401-418 (1971). [DOI], [ADS]. (Cited on pages 11, 13, 46, and 62.) · doi:10.1063/1.1665603
[114] Burke, WL; Thorne, KS; Carmeli, M. (ed.); Fickler, SI (ed.); Witten, L. (ed.), Gravitational Radiation Damping, Proceedings of the Relativity Conference in the Midwest, Cincinnati, Ohio, June 2-6, 1969, New York; London · doi:10.1007/978-1-4684-0721-1_12
[115] Campanelli, M., “Understanding the fate of merging supermassive black holes”, Class. Quantum Grav., 22, S387 (2005). [DOI], [astro-ph/0411744]. (Cited on page 22.) · Zbl 1071.83538 · doi:10.1088/0264-9381/22/10/034
[116] Campanelli, M., Lousto, C. O., Marronetti, P. and Zlochower, Y., “Accurate Evolutions of Orbiting Black-Hole Binaries without Excision”, Phys. Rev. Lett., 96, 111101 (2006). [DOI], [ADS], [arXiv:gr-qc/0511048]. (Cited on page 8.) · doi:10.1103/PhysRevLett.96.111101
[117] Campanelli, M., Lousto, C. O., Zlochower, Y. and Merritt, D., “Large merger recoils and spin flips from generic black-hole binaries”, Astrophys. J. Lett., 659, L5-L8 (2007). [DOI], [arXiv:gr-qc/0701164 [gr-qc]]. (Cited on page 22.) · doi:10.1086/516712
[118] Campbell, W. B., Macek, J. and Morgan, T. A., “Relativistic time-dependent multipole analysis for scalar, electromagnetic, and gravitational fields”, Phys. Rev. D, 15, 2156-2164 (1977). [DOI]. (Cited on page 10.) · doi:10.1103/PhysRevD.15.2156
[119] Campbell, W. B. and Morgan, T. A., “Debye Potentials For Gravitational Field”, Physica, 53(2), 264 (1971). [DOI]. (Cited on page 10.) · doi:10.1016/0031-8914(71)90074-7
[120] Carmeli, M., “The equations of motion of slowly moving particles in the general theory of relativity”, Nuovo Cimento, 37, 842 (1965). [DOI]. (Cited on page 97.) · Zbl 0125.45205 · doi:10.1007/BF02773176
[121] Caudill, M., Cook, G. B., Grigsby, J. D. and Pfeiffer, H. P., “Circular orbits and spin in black-hole initial data”, Phys. Rev. D, 74, 064011 (2006). [DOI], [ADS], [gr-qc/0605053]. (Cited on pages 101, 103, 104, and 110.) · doi:10.1103/PhysRevD.74.064011
[122] Chandrasekhar, S., “The Post-Newtonian Equations of Hydrodynamics in General Relativity”, Astrophys. J., 142, 1488-1540 (1965). [DOI], [ADS]. (Cited on pages 9 and 53.) · doi:10.1086/148432
[123] Chandrasekhar, S. and Esposito, F. P., “The 2½-Post-Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity”, Astrophys. J., 160, 153-179 (1970). [DOI]. (Cited on pages 9 and 53.) · doi:10.1086/150414
[124] Chandrasekhar, S. and Nutku, Y., “The Second Post-Newtonian Equations of Hydrodynamics in General Relativity”, Astrophys. J., 158, 55-79 (1969). [DOI]. (Cited on pages 9 and 53.) · doi:10.1086/150171
[125] Chatziioannou, K., Poisson, E. and Yunes, N., “Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling”, Phys. Rev. D, 87, 044022 (2013). [DOI], [ADS], [arXiv:1211.1686 [gr-qc]]. (Cited on page 158.) · doi:10.1103/PhysRevD.87.044022
[126] Chicone, C., Kopeikin, S. M., Mashhoon, B. and Retzloff, D. G., “Delay equations and radiation damping”, Phys. Lett. A, 285, 17-26 (2001). [DOI], [gr-qc/0101122]. (Cited on page 55.) · Zbl 0969.78506 · doi:10.1016/S0375-9601(01)00327-9
[127] Christodoulou, D., “Reversible and irreversible transformations in black-hole physics”, Phys. Rev. Lett., 25, 1596 (1970). [DOI]. (Cited on page 101.) · doi:10.1103/PhysRevLett.25.1596
[128] Christodoulou, D., “Nonlinear Nature of Gravitation and Gravitational-Wave Experiments”, Phys. Rev. Lett., 67, 1486-1489 (1991). [DOI]. (Cited on pages 21 and 43.) · Zbl 0990.83504 · doi:10.1103/PhysRevLett.67.1486
[129] Christodoulou, D. and Ruffini, R., “Reversible transformations of a charged black hole”, Phys. Rev. D, 4, 3552-3555 (1971). [DOI]. (Cited on page 101.) · doi:10.1103/PhysRevD.4.3552
[130] Christodoulou, D. and Schmidt, B. G., “Convergent and Asymptotic Iteration Methods in General Relativity”, Commun. Math. Phys., 68, 275-289 (1979). [DOI]. (Cited on page 28.) · doi:10.1007/BF01221128
[131] Collins, J. C., Renormalization: An introduction to renormalization, the renormalization group, and the operator-product expansion, (Cambridge University Press, Cambridge; New York, 1984). [Google Books]. (Cited on page 72.) · Zbl 1094.53505 · doi:10.1017/CBO9780511622656
[132] Cook, G. B., “Three-dimensional initial data for the collision of two black holes. II. Quasicircular orbits for equal-mass black holes”, Phys. Rev. D, 50, 5025-5032 (1994). [DOI], [ADS]. (Cited on pages 103 and 104.) · doi:10.1103/PhysRevD.50.5025
[133] Cook, G. B. and Pfeiffer, H. P., “Excision boundary conditions for black hole initial data”, Phys. Rev. D, 70, 104016 (2004). [DOI], [ADS]. (Cited on pages 101, 102, 103, 104, and 110.) · doi:10.1103/PhysRevD.70.104016
[134] Cooperstock, F. I. and Booth, D. J., “Angular-Momentum Flux For Gravitational Radiation to Octupole Order”, Nuovo Cimento B, 62(1), 163-170 (1969). [DOI]. (Cited on page 10.) · doi:10.1007/BF02712475
[135] Corinaldesi, E. and Papapetrou, A., “Spinning test-particles in general relativity. II”, Proc. R. Soc. London, Ser. A, 209, 259-268 (1951). [DOI]. (Cited on pages 148 and 150.) · Zbl 0044.22802 · doi:10.1098/rspa.1951.0201
[136] Crowley, R. J. and Thorne, K. S., “Generation of gravitational waves. II. Post-linear formalism revisited”, Astrophys. J., 215, 624-635 (1977). [DOI]. (Cited on page 10.) · doi:10.1086/155397
[137] Cutler, C., Finn, L. S., Poisson, E. and Sussman, G. J., “Gravitational radiation from a particle in circular orbit around a black hole. II. Numerical results for the nonrotating case”, Phys. Rev. D, 47, 1511-1518 (1993). [DOI]. (Cited on pages 16, 65, and 125.) · doi:10.1103/PhysRevD.47.1511
[138] Cutler, C. and Flanagan, É. É., “Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral wave form?”, Phys. Rev. D, 49, 2658-2697 (1994). [DOI], [arXiv:gr-qc/9402014]. (Cited on pages 14, 16, 65, 124, 125, and 146.) · doi:10.1103/PhysRevD.49.2658
[139] Cutler, C. et al., “The Last Three Minutes: Issues in Gravitational-Wave Measurements of Coalescing Compact Binaries”, Phys. Rev. Lett., 70, 2984-2987 (1993). [DOI], [astro-ph/9208005]. (Cited on pages 14, 16, 65, and 125.) · doi:10.1103/PhysRevLett.70.2984
[140] D’Alembert, J., Traité de Dynamique, (David L’Aine, Paris, 1743). [Google Books]. (Cited on page 7.) · JFM 48.1113.03
[141] Damour, T., “Problème des deux corps et freinage de rayonnement en relativité générale”, C. R. Acad. Sci. Ser. II, 294, 1355-1357 (1982). (Cited on page 17.)
[142] Damour, T.; Deruelle, N. (ed.); Piran, T. (ed.), Gravitational radiation and the motion of compact bodies, Proceedings of the Les Houches Summer School, 2-21 June 1982, Amsterdam
[143] Damour, T., “Gravitational radiation reaction in the binary pulsar and the quadrupole formula controvercy”, Phys. Rev. Lett., 51, 1019-1021 (1983). [DOI]. (Cited on pages 7, 17, and 135.) · doi:10.1103/PhysRevLett.51.1019
[144] Damour, T.; Carter, B. (ed.); Hartle, JB (ed.), An Introduction to the Theory of Gravitational Radiation, Proceedings of a NATO Advanced Study Institute on Gravitation in Astrophysics, Cargese, France, 15-31 July, 1986, New York · doi:10.1007/978-1-4613-1897-2_1
[145] Damour, T.; Hawking, SW (ed.); Israel, W. (ed.), The problem of motion in Newtonian and Einsteinian gravity, 128-198 (1987), Cambridge; New York · Zbl 0966.83509
[146] Damour, T., “Gravitational self-force in a Schwarzschild background and the effective one-body formalism”, Phys. Rev. D, 81, 024017 (2010). [DOI], [arXiv:0910.5533 [gr-qc]]. (Cited on page 114.) · doi:10.1103/PhysRevD.81.024017
[147] Damour, T. and Deruelle, N., “Lagrangien généralisé du système de deux masses ponctuelles, à l’approximation post-post-newtonienne de la relativité générale”, C. R. Acad. Sci. Ser. II, 293, 537-540 (1981). (Cited on pages 7, 17, and 84.)
[148] Damour, T. and Deruelle, N., “Radiation reaction and angular momentum loss in small angle gravitational scattering”, Phys. Lett. A, 87, 81-84 (1981). [DOI]. (Cited on pages 7 and 17.) · doi:10.1016/0375-9601(81)90567-3
[149] Damour, T. and Deruelle, N., “General relativistic celestial mechanics of binary systems I. The post-Newtonian motion”, Ann. Inst. Henri Poincare A, 43, 107’132 (1985). Online version (accessed 17 October 2013): http://www.numdam.org/item?id=AIHPA_1985__43_1_107_0. (Cited on pages 135, 137, 138, and 140.) · Zbl 0585.70010
[150] Damour, T. and Deruelle, N., “General relativistic celestial mechanics of binary systems II. The post-Newtonian timing formula”, Ann. Inst. Henri Poincare A, 44, 263-292 (1986). Online version (accessed 17 October 2013): http://www.numdam.org/item?id=AIHPA_1986__44_3_263_0. (Cited on page 137.) · Zbl 0617.70010
[151] Damour, T. and Esposito-Farèse, G., “Testing gravity to second post-Newtonian order: A field-theory approach”, Phys. Rev. D, 53, 5541-5578 (1996). [DOI], [ADS], [gr-qc/9506063]. (Cited on pages 18 and 71.) · doi:10.1103/PhysRevD.53.5541
[152] Damour, T. and Gopakumar, A., “Gravitational recoil during binary black hole coalescence using the effective one body approach”, Phys. Rev. D, 73, 124006 (2006). [DOI], [gr-qc/0602117]. (Cited on page 22.) · doi:10.1103/PhysRevD.73.124006
[153] Damour, T., Gopakumar, A. and Iyer, B. R., “Phasing of gravitational waves from inspiralling eccentric binaries”, Phys. Rev. D, 70, 064028 (2004). [DOI], [gr-qc/0404128]. (Cited on pages 141, 145, and 146.) · Zbl 1071.83516 · doi:10.1103/PhysRevD.70.064028
[154] Damour, T. and Iyer, B. R., “Multipole analysis for electromagnetism and linearized gravity with irreducible Cartesian tensors”, Phys. Rev. D, 43, 3259-3272 (1991). [DOI]. (Cited on pages 10 and 51.) · doi:10.1103/PhysRevD.43.3259
[155] Damour, T. and Iyer, B. R., “Post-Newtonian generation of gravitational waves. II. The spin moments”, Ann. Inst. Henri Poincare A, 54, 115-164 (1991). Online version (accessed 17 October 2013): http://www.numdam.org/item?id=AIHPA_1991__54_2_115_0. (Cited on pages 11 and 46.) · Zbl 0746.53056
[156] Damour, T., Iyer, B. R., Jaranowski, P. and Sathyaprakash, B. S., “Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates”, Phys. Rev. D, 67, 064028 (2003). [DOI], [gr-qc/0211041]. (Cited on pages 65, 71, and 131.) · doi:10.1103/PhysRevD.67.064028
[157] Damour, T., Iyer, B. R. and Sathyaprakash, B. S., “Improved filters for gravitational waves from inspiraling compact binaries”, Phys. Rev. D, 57, 885-907 (1998). [DOI], [gr-qc/9708034]. (Cited on pages 16 and 65.) · doi:10.1103/PhysRevD.57.885
[158] Damour, T., Iyer, B. R. and Sathyaprakash, B. S., “Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries”, Phys. Rev. D, 62, 084036 (2000). [DOI], [gr-qc/0001023]. (Cited on page 65.) · doi:10.1103/PhysRevD.62.084036
[159] Damour, T., Iyer, B. R. and Sathyaprakash, B. S., “Comparison of search templates for gravitational waves from binary inspiral: 3.5PN update”, Phys. Rev. D, 66, 027502 (2002). [DOI], [gr-qc/0207021]. (Cited on pages 65, 71, and 131.) · doi:10.1103/PhysRevD.66.027502
[160] Damour, T., Jaranowski, P. and Schäfer, G., “Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation”, Phys. Rev. D, 62, 044024 (2000). [gr-qc/9912092]. (Cited on pages 95 and 110.) · doi:10.1103/PhysRevD.62.044024
[161] Damour, T., Jaranowski, P. and Schäafer, G., “On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation”, Phys. Rev. D, 62, 084011 (2000). [ADS], [gr-qc/0005034]. (Cited on page 65.) · doi:10.1103/PhysRevD.62.084011
[162] Damour, T., Jaranowski, P. and Schäfer, G., “Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem”, Phys. Rev. D, 62, 021501(R) (2000). [gr-qc/0003051]. Erratum: Phys. Rev. D, 63, 029903(E) (2000). (Cited on pages 17, 18, 69, 88, and 93.) · doi:10.1103/PhysRevD.62.021501
[163] Damour, T., Jaranowski, P. and Schäafer, G., “Dimensional regularization of the gravitational interaction of point masses”, Phys. Lett. B, 513, 147-155 (2001). [DOI], [gr-qc/0105038]. (Cited on pages 18, 70, 74, and 76.) · Zbl 0969.83506 · doi:10.1016/S0370-2693(01)00642-6
[164] Damour, T., Jaranowski, P. and Schäafer, G., “Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries”, Phys. Rev. D, 63, 044021 (2001). [DOI], [gr-qc/0010040]. Erratum: Phys. Rev. D, 66, 029901(E) (2002). (Cited on pages 17, 18, and 70.) · doi:10.1103/PhysRevD.63.044021
[165] Damour, T., Jaranowski, P. and Schäafer, G., “Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling”, Phys. Rev. D, 77, 064032 (2008). [DOI], [arXiv:0711.1048]. (Cited on pages 19, 147, and 151.) · doi:10.1103/PhysRevD.77.064032
[166] Damour, T., Jaranowski, P. and Schäafer, G., “Non-local-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems”, Phys. Rev. D, 89, 064058 (2014). [DOI], [arXiv:1401.4548 [gr-qc]]. (Cited on page 19.) · doi:10.1103/PhysRevD.89.064058
[167] Damour, T., Jaranowski, P. and Schäfer, G., “Fourth post-Newtonian effective one-body dynamics”, Phys. Rev. D, 91, 084024 (2015). [DOI], [arXiv:1502.07245 [gr-qc]]. (Cited on page 19.) · doi:10.1103/PhysRevD.91.084024
[168] Damour, T.; Nagar, A.; Blanchet, L. (ed.); Spallicci, A. (ed.); Whiting, B. (ed.), The Effective One-Body description of the Two-Body Problem, Lectures from the CNRS School on Mass, Orlreans, France, 23-25 June 2008, Dordrecht; New York · Zbl 1213.83036
[169] Damour, T. and Schäfer, G., “Lagrangians for <Emphasis Type=”Italic“>n Point Masses at the Second Post-Newtonian Approximation of General Relativity”, Gen. Relativ. Gravit., 17, 879-905 (1985). [DOI]. (Cited on pages 17 and 85.) · Zbl 0568.70014
[170] Damour, T. and Schäafer, G., “Higher-Order Relativistic Periastron Advances in Binary Pulsars”, Nuovo Cimento B, 101, 127-176 (1988). [DOI]. (Cited on pages 138, 139, and 141.) · doi:10.1007/BF02828697
[171] Damour, T. and Schmidt, B. G., “Reliability of perturbation theory in general relativity”, J. Math. Phys., 31, 2441-2458 (1990). [DOI]. (Cited on page 28.) · Zbl 0723.53050 · doi:10.1063/1.528850
[172] Damour, T., Soffel, M. and Xu, C., “General-relativistic celestial mechanics. I. Method and definition of reference systems”, Phys. Rev. D, 43, 3273-3307 (1991). [DOI], [ADS]. (Cited on page 70.) · doi:10.1103/PhysRevD.43.3273
[173] Damour, T. and Taylor, J. H., “On the Orbital Period Change of the Binary Pulsar PSR 1913+16”, Astrophys. J., 366, 501-511 (1991). [DOI], [ADS]. (Cited on page 17.) · doi:10.1086/169585
[174] de Andrade, V. C., Blanchet, L. and Faye, G., “Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms”, Class. Quantum Grav., 18, 753-778 (2001). [DOI], [gr-qc/0011063]. (Cited on pages 17, 18, 71, 85, 86, 87, 88, and 90.) · Zbl 0973.83016 · doi:10.1088/0264-9381/18/5/301
[175] Deruelle, N., Sur les equations du mouvement et le rayonnement gravitationnel d’un système binaire en Relativité Générale, Ph.D. thesis, (Université Pierre et Marie Curie, Paris, 1982). (Cited on page 17.)
[176] Detweiler, S., “Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry”, Phys. Rev. D, 77, 124026 (2008). [DOI], [arXiv:0804.3529]. (Cited on pages 109, 112, 114, and 115.) · doi:10.1103/PhysRevD.77.124026
[177] Detweiler, S.; Blanchet, L. (ed.); Spallicci, A. (ed.); Whiting, B. (ed.), Elementary Development of the Gravitational Self-Force, Lectures from the CNRS School on Mass, Orléans, France, 23-25 June 2008, Dordrecht; New York · Zbl 1213.83037
[178] Detweiler, S. and Whiting, B. F., “Self-force via a Green’s function decomposition”, Phys. Rev. D, 67, 024025 (2003). [DOI], [arXiv:gr-qc/0202086]. (Cited on pages 112 and 115.) · doi:10.1103/PhysRevD.67.024025
[179] Dixon, WG; Ehlers, J. (ed.), Extended bodies in general relativity: Their description and motion, Proceedings of the International School of Physics ‘Enrico Fermi’, Course 67, Varenna on Lake Como, Villa Monastero, Italy, 28 June-10 July, 1976, Amsterdam; New York
[180] Eder, E., “Existence, uniqueness and iterative construction of motions of charged particles with retarded interactions”, Ann. Inst. Henri Poincare A, 39, 1-27 (1983). Online version (accessed 17 October 2013): http://www.numdam.org/item?id=AIHPA_1983__39_1_1_0. (Cited on page 38.) · Zbl 0516.34066
[181] Ehlers, J., “Isolated systems in general relativity”, Ann. N.Y. Acad. Sci., 336, 279-294 (1980). [DOI]. (Cited on pages 53 and 57.) · doi:10.1111/j.1749-6632.1980.tb15936.x
[182] Ehlers, J., Rosenblum, A., Goldberg, J. N. and Havas, P., “Comments on gravitational radiation damping and energy loss in binary systems”, Astrophys. J. Lett., 208, L77-L81 (1976). [DOI], [ADS]. (Cited on page 54.) · doi:10.1086/182236
[183] Einstein, A., “Über Gravitationswellen”, Sitzungsber. K. Preuss. Akad. Wiss., 1918, 154-167 (1918). [ADS]. Online version (accessed 31 January 2014): http://echo.mpiwg-berlin.mpg.de/MPIWG:8HSP60BU. (Cited on pages 9 and 12.) · JFM 46.1295.02
[184] Einstein, A., Infeld, L. and Hoffmann, B., “The Gravitational Equations and the Problem of Motion”, Ann. Math. (2), 39, 65-100 (1938). [DOI]. (Cited on pages 7, 17, and 70.) · Zbl 0018.28103 · doi:10.2307/1968714
[185] Epstein, R. and Wagoner, R. V., “Post-Newtonian Generation of Gravitational Waves”, Astrophys. J., 197, 717-723 (1975). [DOI], [ADS]. (Cited on pages 11, 20, and 50.) · doi:10.1086/153561
[186] Esposito, L. W. and Harrison, E. R., “Properties of the Hulse-Taylor binary pulsar system”, Astrophys. J. Lett., 196, L1-L2 (1975). [DOI]. (Cited on page 13.) · doi:10.1086/181729
[187] Faber, J. A. and Rasio, F. A., “Binary Neutron Star Mergers”, Living Rev. Relativity, 15, lrr-2012-8 (2012). [DOI], [ADS], [arXiv:1204.3858 [gr-qc]]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2012-8. (Cited on pages 8 and 16.)
[188] Fabian, AC; Miniutti, G.; Wiltshire, DL (ed.); Visser, M. (ed.); Scott, SM (ed.), The X-ray spectra of accreting Kerr black holes (2009), Cambridge; New York · Zbl 1171.85002
[189] Favata, M., “Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries”, Phys. Rev. D, 80, 024002 (2009). [DOI], [ADS], [arXiv:0812.0069]. (Cited on pages 21, 43, 130, and 134.) · doi:10.1103/PhysRevD.80.024002
[190] Favata, M., “Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force”, Phys. Rev. D, 83, 024028 (2011). [DOI], [arXiv:1010.2553]. (Cited on page 108.) · doi:10.1103/PhysRevD.83.024028
[191] Favata, M., “Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods”, Phys. Rev. D, 83, 024027 (2011). [DOI], [arXiv:1008.4622]. (Cited on page 108.) · doi:10.1103/PhysRevD.83.024027
[192] Favata, M., “The gravitational-wave memory from eccentric binaries”, Phys. Rev. D, 84, 124013 (2011). [DOI], [arXiv:1108.3121]. (Cited on pages 21 and 43.) · doi:10.1103/PhysRevD.84.124013
[193] Faye, G., Equations du mouvement d’un systeme binaire d’objets compact à l’approximation post-newtonienne, Ph.D. thesis, (Université Paris VI, Paris, 1999). (Cited on page 75.)
[194] Faye, G., Blanchet, L. and Buonanno, A., “Higher-order spin effects in the dynamics of compact binaries I. Equations of motion”, Phys. Rev. D, 74, 104033 (2006). [DOI], [gr-qc/0605139]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.74.104033
[195] Faye, G., Blanchet, L. and Iyer, B. R., “Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order”, Class. Quantum Grav., 32, 045016 (2015). [arXiv:1409.3546 [gr-qc]]. (Cited on page 132.) · Zbl 1308.83089 · doi:10.1088/0264-9381/32/4/045016
[196] Faye, G., Jaranowski, P. and Schäfer, G., “Skeleton approximate solution of the Einstein field equations for multiple black-hole systems”, Phys. Rev. D, 69, 124029 (2004). [DOI], [gr-qc/0311018]. (Cited on page 103.) · doi:10.1103/PhysRevD.69.124029
[197] Faye, G., Marsat, S., Blanchet, L. and Iyer, B. R., “The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries”, Class. Quantum Grav., 29, 175004 (2012). [DOI], [arXiv:1204.1043]. (Cited on pages 11, 20, 31, 40, 44, 45, 117, 118, 125, 131, and 132.) · Zbl 1251.83012 · doi:10.1088/0264-9381/29/17/175004
[198] Finn, L. S. and Chernoff, D. F., “Observing binary inspiral in gravitational radiation: One interferometer”, Phys. Rev. D, 47, 2198-2219 (1993). [DOI], [arXiv:gr-qc/9301003]. (Cited on pages 16 and 65.) · doi:10.1103/PhysRevD.47.2198
[199] Fitchett, M. J., “The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system”, Mon. Not. R. Astron. Soc., 203, 1049-1062 (1983). [ADS]. (Cited on page 22.) · Zbl 0533.70007 · doi:10.1093/mnras/203.4.1049
[200] Flanagan, É.É.. and Hinderer, T., “Constraining neutron star tidal Love numbers with gravitational wave detectors”, Phys. Rev. D, 77, 021502 (2008). [DOI], [ADS], [arXiv:0709.1915 [astro-ph]]. (Cited on page 16.) · doi:10.1103/PhysRevD.77.021502
[201] Fock, V. A., “On motion of finite masses in general relativity”, J. Phys. (Moscow), 1(2), 81-116 (1939). (Cited on page 17.) · JFM 65.1047.04
[202] Fock, V. A., Theory of space, time and gravitation, (Pergamon, London, 1959). (Cited on pages 33 and 97.) · Zbl 0085.42301
[203] Foffa, S. and Sturani, R., “Effective field theory calculation of conservative binary dynamics at third post-Newtonian order”, Phys. Rev. D, 84, 044031 (2011). [DOI], [arXiv:1104.1122 [gr-qc]]. (Cited on pages 18 and 71.) · doi:10.1103/PhysRevD.84.044031
[204] Foffa, S. and Sturani, R., “The dynamics of the gravitational two-body problem in the post-Newtonian approximation at quadratic order in the Newton’s constant”, Phys. Rev. D, 87, 064011 (2012). [arXiv:1206.7087 [gr-qc]]. (Cited on pages 19 and 96.) · doi:10.1103/PhysRevD.87.064011
[205] Foffa, S. and Sturani, R., “Tail terms in gravitational radiation reaction via effective field theory”, Phys. Rev. D, 87, 044056 (2013). [DOI], [arXiv:1111.5488 [gr-qc]]. (Cited on page 19.) · doi:10.1103/PhysRevD.87.044056
[206] Foffa, S. and Sturani, R., “Effective field theory methods to model compact binaries”, Class. Quantum Grav., 31, 043001 (2014). [DOI], [ADS], [arXiv:1309.3474 [gr-qc]]. (Cited on page 18.) · Zbl 1286.83034 · doi:10.1088/0264-9381/31/4/043001
[207] Fokker, A. D., “Ein invarianter Variationssatz für die Bewegung mehrerer elektrischer Massenteilchen”, Z. Phys., 58, 386-393 (1929). [DOI], [ADS]. (Cited on page 18.) · JFM 55.0522.03 · doi:10.1007/BF01340389
[208] Friedman, J. L., Uryū, K. and Shibata, M., “Thermodynamics of binary black holes and neutron stars”, Phys. Rev. D, 65, 064035 (2002). [DOI]. Erratum: Phys. Rev. D, 70, 129904(E) (2004). (Cited on pages 108, 110, and 112.) · doi:10.1103/PhysRevD.65.064035
[209] Fujita, R., “Gravitational Radiation for Extreme Mass Ratio Inspirals to the 14th Post-Newtonian Order”, Prog. Theor. Phys., 127, 583-590 (2012). [DOI], [arXiv:1104.5615 [gr-qc]]. (Cited on page 21.) · Zbl 1250.83026 · doi:10.1143/PTP.127.583
[210] Fujita, R., “Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order”, Prog. Theor. Phys., 128, 971-992 (2012). [DOI], [ADS], [arXiv:1211.5535 [gr-qc]]. (Cited on page 21.) · doi:10.1143/PTP.128.971
[211] Futamase, T., “Gravitational radiation reaction in the Newtonian limit”, Phys. Rev. D, 28, 2373-2381 (1983). [DOI]. (Cited on page 54.) · doi:10.1103/PhysRevD.28.2373
[212] Futamase, T., “Strong-field point-particle limit and the equations of motion in the binary pulsar”, Phys. Rev. D, 36, 321-329 (1987). [DOI]. (Cited on page 70.) · doi:10.1103/PhysRevD.36.321
[213] Futamase, T. and Itoh, Y., “The Post-Newtonian Approximation for Relativistic Compact Binaries”, Living Rev. Relativity, 10, lrr-2007-2 (2007). [DOI], [ADS]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2007-2. (Cited on page 17.) · Zbl 1255.83005
[214] Futamase, T. and Schutz, B. F., “Newtonian and post-Newtonian approximations are asymptotic to general relativity”, Phys. Rev. D, 28, 2363-2372 (1983). [DOI]. (Cited on page 54.) · doi:10.1103/PhysRevD.28.2363
[215] Galley, C. R., Leibovich, A. K., Porto, R. A. and Ross, A., “The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution”, arXiv, e-print, (2015). [arXiv:1511.07379 [gr-qc]]. (Cited on page 19.) · Zbl 1169.83301
[216] Gal’tsov, D. V., Matiukhin, A. A. and Petukhov, V. I., “Relativistic corrections to the gravitational radiation of a binary system and the fine structure of the spectrum”, Phys. Lett. A, 77, 387-390 (1980). [DOI]. (Cited on page 21.) · doi:10.1016/0375-9601(80)90728-8
[217] Gergely, L.Á., “Spin-spin effects in radiating compact binaries”, Phys. Rev. D, 61, 024035 (1999). [DOI], [gr-qc/9911082]. (Cited on page 147.) · doi:10.1103/PhysRevD.61.024035
[218] Gergely, L.Á., “Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries”, Phys. Rev. D, 62, 024007 (2000). [DOI], [gr-qc/0003037]. (Cited on pages 147 and 159.) · doi:10.1103/PhysRevD.62.024007
[219] Geroch, R., “Multipole Moments. II. Curved Space”, J. Math. Phys., 11, 2580-2588 (1970). [DOI], [ADS]. (Cited on page 10.) · Zbl 1107.83312 · doi:10.1063/1.1665427
[220] Geroch, R. and Horowitz, G. T., “Asymptotically simple does not imply asymptotically Minkowskian”, Phys. Rev. Lett., 40, 203-206 (1978). (Cited on pages 10, 11, 34, and 35.) · doi:10.1103/PhysRevLett.40.203
[221] Goldberger, W. D. and Ross, A., “Gravitational radiative corrections from effective field theory”, Phys. Rev. D, 81, 124015 (2010). [DOI], [arXiv:0912.4254]. (Cited on page 20.) · doi:10.1103/PhysRevD.81.124015
[222] Goldberger, W. D., Ross, A. and Rothstein, I. Z., “Black hole mass dynamics and renormalization group evolution”, Phys. Rev. D, 89, 124033 (2014). [DOI], [ADS], [arXiv:1211.6095 [hep-th]]. (Cited on pages 18 and 44.) · doi:10.1103/PhysRevD.89.124033
[223] Goldberger, W. D. and Rothstein, I. Z., “Effective field theory of gravity for extended objects”, Phys. Rev. D, 73, 104029 (2006). [DOI], [arXiv:hep-th/0409156 [hep-th]]. (Cited on pages 18, 71, and 72.) · doi:10.1103/PhysRevD.73.104029
[224] Gopakumar, A. and Iyer, B. R., “Gravitational waves from inspiraling compact binaries: Angular momentum flux, evolution of the orbital elements and the waveform to the second post-Newtonian order”, Phys. Rev. D, 56, 7708-7731 (1997). [DOI], [arXiv:gr-qc/9710075]. (Cited on pages 20, 140, and 145.) · doi:10.1103/PhysRevD.56.7708
[225] Gopakumar, A. and Iyer, B. R., “Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits”, Phys. Rev. D, 65, 084011 (2002). [DOI], [arXiv:gr-qc/0110100]. (Cited on page 140.) · doi:10.1103/PhysRevD.65.084011
[226] Gopakumar, A., Iyer, B. R. and Iyer, S., “Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies”, Phys. Rev. D, 55, 6030-6053 (1997). [DOI], [arXiv:gr-qc/9703075]. (Cited on page 18.) · doi:10.1103/PhysRevD.55.6030
[227] Gou, L. et al., “The extreme spin of the black hole in Cygnus X-1”, Astrophys. J., 742, 85 (2011). [DOI], [arXiv:1106.3690 [astro-ph.HE]]. (Cited on page 146.) · doi:10.1088/0004-637X/742/2/85
[228] Gourgoulhon, E., Grandclément, P. and Bonazzola, S., “Binary black holes in circular orbits. I. A global spacetime approach”, Phys. Rev. D, 65, 044020 (2002). [DOI], [ADS], [gr-qc/0106015]. (Cited on pages 101, 103, 104, and 110.) · Zbl 0988.65108 · doi:10.1103/PhysRevD.65.044020
[229] Gourgoulhon, E., Grandclément, P., Taniguchi, K., Marck, J.-A. and Bonazzola, S., “Quasi-equilibrium sequences of synchronized and irrotational binary neutron stars in general relativity”, Phys. Rev. D, 63, 064029 (2001). [DOI], [gr-qc/0007028]. (Cited on page 101.) · Zbl 0988.65108 · doi:10.1103/PhysRevD.63.064029
[230] Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, (Academic Press, San Diego; London, 1980). (Cited on page 121.) · Zbl 0521.33001
[231] Gralla, S. E. and Wald, R. M., “A rigorous derivation of gravitational self-force”, Class. Quantum Grav., 25, 205009 (2008). [DOI], [arXiv:0806.3293]. (Cited on page 112.) · Zbl 1152.83405 · doi:10.1088/0264-9381/25/20/205009
[232] Grandclément, P., Gourgoulhon, E. and Bonazzola, S., “Binary black holes in circular orbits. II. Numerical methods and first results”, Phys. Rev. D, 65, 044021 (2002). [DOI], [ADS]. (Cited on pages 101, 102, 103, 104, and 110.) · doi:10.1103/PhysRevD.65.044021
[233] Grandclément, P. and Novak, J., “Spectral Methods for Numerical Relativity”, Living Rev. Relativity, 12, lrr-2009-1 (2009). [DOI], [ADS], [arXiv:0706.2286 [gr-qc]]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2009-1. (Cited on page 8.) · Zbl 1166.83004
[234] Grishchuk, LP; Kopeikin, SM; Kovalevsky, J. (ed.); Brumberg, VA (ed.), Equations of motion for isolated bodies with relativistic corrections including the radiation-reaction force, Proceedings of the 114th Symposium of the International Astronomical Union, Leningrad, USSR, May 28-31, 1985, Dordrecht; Boston · doi:10.1007/978-94-009-4602-6_3
[235] Gultekin, K., Miller, M. C. and Hamilton, D. P., “Growth of Intermediate-Mass Black Holes in Globular Clusters”, Astrophys. J., 616, 221 (2004). [DOI], [astro-ph/0402532]. (Cited on pages 135 and 145.) · doi:10.1086/424809
[236] Hadamard, J., Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques, (Hermann, Paris, 1932). (Cited on pages 7 and 66.) · JFM 58.0519.16
[237] Hannam, M., Husa, S., González, J. A., Sperhake, U. and Brügmann, B., “Where post-Newtonian and numerical-relativity waveforms meet”, Phys. Rev. D, 77, 044020 (2008). [DOI], [ADS], [arXiv:0706.1305]. (Cited on page 36.) · doi:10.1103/PhysRevD.77.044020
[238] Hansen, R. O., “Multipole moments of stationary space-times”, J. Math. Phys., 15, 46-52 (1974). [DOI], [ADS]. (Cited on page 10.) · Zbl 1107.83304 · doi:10.1063/1.1666501
[239] Hanson, A. J. and Regge, T., “The Relativistic Spherical Top”, Ann. Phys. (N.Y.), 87, 498-566 (1974). [DOI]. (Cited on pages 148 and 150.) · doi:10.1016/0003-4916(74)90046-3
[240] Hari Dass, N. D. and Soni, V., “Feynman graph derivation of the Einstein quadrupole formula”, J. Phys. A: Math. Gen., 15, 473-492 (1982). [DOI]. (Cited on page 18.) · doi:10.1088/0305-4470/15/2/019
[241] Hartung, J. and Steinhoff, J., “Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for <Emphasis Type=”Italic“>n gravitating spinning compact objects”, Phys. Rev. D, 83, 044008 (2011). [DOI], [arXiv:1011.1179 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.83.044008
[242] Hartung, J. and Steinhoff, J., “Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries”, Ann. Phys. (Berlin), 523, 783-790 (2011). [DOI], [ADS], [arXiv:1104.3079 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1316.70017 · doi:10.1002/andp.201100094
[243] Hartung, J. and Steinhoff, J., “Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries”, Ann. Phys. (Berlin), 523, 919-924 (2011). [DOI], [ADS], [arXiv:1107.4294 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1326.70028 · doi:10.1002/andp.201100163
[244] Hartung, J., Steinhoff, J. and Schäfer, G., “Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians”, Ann. Phys. (Berlin), 525, 359-394 (2013). [DOI], [ADS], [arXiv:1302.6723 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1269.83016 · doi:10.1002/andp.201200271
[245] Hergt, S. and Schäafer, G., “Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance”, Phys. Rev. D, 78, 124004 (2008). [DOI], [arXiv:0809.2208 [gr-qc]]. (Cited on page 147.) · doi:10.1103/PhysRevD.78.124004
[246] Hergt, S. and Schäfer, G., “Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates”, Phys. Rev. D, 77, 104001 (2008). [DOI], [arXiv:0712.1515 [gr-qc]]. (Cited on page 147.) · doi:10.1103/PhysRevD.77.104001
[247] Hergt, S., Steinhoff, J. and Schäfer, G., “The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries”, Class. Quantum Grav., 27, 135007 (2010). [DOI], [arXiv:1002.2093 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1195.83080 · doi:10.1088/0264-9381/27/13/135007
[248] Hopper, S., Kavanagh, C. and Ottewill, A. C., “Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background”, Phys. Rev. D, 93, 044010 (2016). [DOI], [arXiv:1512.01556 [gr-qc]]. (Cited on page 19.) · doi:10.1103/PhysRevD.93.044010
[249] Hotokezaka, K., Kyutoku, K. and Shibata, M., “Exploring tidal effects of coalescing binary neutron stars in numerical relativity”, Phys. Rev. D, 87, 044001 (2013). [DOI], [arXiv:1301.3555 [gr-qc]]. (Cited on page 16.) · doi:10.1103/PhysRevD.87.044001
[250] Hulse, R. A. and Taylor, J. H., “Discovery of a pulsar in a binary system”, Astrophys. J., 195, L51-L53 (1975). [DOI], [ADS]. (Cited on page 7.) · Zbl 1192.82066 · doi:10.1086/181708
[251] Hunter, A. J. and Rotenberg, M. A., “The double-series approximation method in general relativity. I. Exact solution of the (24) approximation. II. Discussion of ‘wave tails’ in the (2s) approximation”, J. Phys. A: Math. Gen., 2, 34-49 (1969). [DOI]. (Cited on pages 10 and 26.) · doi:10.1088/0305-4470/2/1/007
[252] Isaacson, R. A. and Winicour, J., “Harmonic and Null Descriptions of Gravitational Radiation”, Phys. Rev., 168, 1451-1456 (1968). [DOI]. (Cited on page 33.) · doi:10.1103/PhysRev.168.1451
[253] Itoh, Y., “Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order”, Phys. Rev. D, 69, 064018 (2004). [DOI]. (Cited on pages 17, 18, 70, and 71.) · doi:10.1103/PhysRevD.69.064018
[254] Itoh, Y., “Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit”, Phys. Rev. D, 80, 124003 (2009). [DOI], [arXiv:0911.4232 [gr-qc]]. (Cited on pages 18, 70, 78, 92, and 117.) · doi:10.1103/PhysRevD.80.124003
[255] Itoh, Y. and Futamase, T., “New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity”, Phys. Rev. D, 68, 121501(R) (2003). [DOI], [gr-qc/0310028]. (Cited on pages 17, 18, 70, and 71.) · doi:10.1103/PhysRevD.68.121501
[256] Itoh, Y….., Futamase, T. and Asada, H., “Equation of motion for relativistic compact binaries with the strong field point particle limit: Formulation, the first post-Newtonian order, and multipole terms”, Phys. Rev. D, 62, 064002 (2000). [DOI], [gr-qc/9910052]. (Cited on pages 17, 18, and 70.) · doi:10.1103/PhysRevD.62.064002
[257] Itoh, Y., Futamase, T. and Asada, H., “Equation of motion for relativistic compact binaries with the strong field point particle limit: The second and half post-Newtonian order”, Phys. Rev. D, 63, 064038 (2001). [DOI], [gr-qc/0101114]. (Cited on pages 17, 18, and 70.) · doi:10.1103/PhysRevD.63.064038
[258] Iyer, B. R. and Will, C. M., “Post-Newtonian gravitational radiation reaction for two-body systems”, Phys. Rev. Lett., 70, 113-116 (1993). [DOI]. (Cited on pages 18, 64, 78, 84, 92, and 117.) · doi:10.1103/PhysRevLett.70.113
[259] Iyer, B. R. and Will, C. M., “Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies”, Phys. Rev. D, 52, 6882-6893 (1995). [DOI]. (Cited on pages 18, 64, 78, 84, 92, and 117.) · doi:10.1103/PhysRevD.52.6882
[260] Jaranowski, P. and Schäafer, G., “Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems”, Phys. Rev. D, 55, 4712-4722 (1997). [DOI]. (Cited on pages 18, 78, 92, and 117.) · doi:10.1103/PhysRevD.55.4712
[261] Jaranowski, P. and Schäafer, G., “Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems”, Phys. Rev. D, 57, 7274-7291 (1998). [DOI], [gr-qc/9712075]. (Cited on pages 17, 68, 69, 86, 87, 88, and 93.) · doi:10.1103/PhysRevD.57.7274
[262] Jaranowski, P. and Schäafer, G., “Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part”, Phys. Rev. D, 60, 124003 (1999). [DOI], [gr-qc/9906092]. (Cited on pages 17, 68, 69, 86, 87, 88, and 93.) · doi:10.1103/PhysRevD.60.124003
[263] Jaranowski, P. and Schäafer, G., “The binary black-hole dynamics at the third post-Newtonian order in the orbital motion”, Ann. Phys. (Berlin), 9, 378-383 (2000). [DOI], [gr-qc/0003054]. (Cited on pages 17, 68, and 88.) · Zbl 0971.83041 · doi:10.1002/(SICI)1521-3889(200005)9:3/5<378::AID-ANDP378>3.0.CO;2-M
[264] Jaranowski, P. and Schäfer, G., “Towards the fourth post-Newtonian Hamiltonian for two-point-mass systems”, Phys. Rev. D, 86, 061503(R) (2012). [DOI], [arXiv:1207.5448 [gr-qc]]. (Cited on pages 19 and 96.) · doi:10.1103/PhysRevD.86.061503
[265] Jaranowski, P. and Schäafer, G., “Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian”, Phys. Rev. D, 87, 081503(R) (2013). [DOI], [arXiv:1303.3225 [gr-qc]]. (Cited on pages 19 and 96.) · doi:10.1103/PhysRevD.87.081503
[266] Jaranowski, P. and Schäfer, G., “Derivation of the local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries”, Phys. Rev. D, 92, 124043 (2015). [DOI], [arXiv:1508.01016 [gr-qc]]. (Cited on page 19.) · doi:10.1103/PhysRevD.92.124043
[267] Junker, W. and Schäfer, G., “Binary systems: higher order gravitational radiation damping and wave emission”, Mon. Not. R. Astron. Soc., 254, 146-164 (1992). [ADS]. (Cited on pages 140 and 145.) · doi:10.1093/mnras/254.1.146
[268] Kavanagh, C., Ottewill, A. C. and Wardell, B., “Analytical high-order post-Newtonian expansions for extreme mass ratio binaries”, Phys. Rev. D, 92, 084025 (2015). [DOI], [ADS], [arXiv:1503.02334 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.92.084025
[269] Kerlick, G. D., “Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part I. First post-Newtonian equations”, Gen. Relativ. Gravit., 12, 467-482 (1980). [DOI]. (Cited on pages 53 and 57.) · doi:10.1007/BF00756177
[270] Kerlick, G. D., “Finite reduced hydrodynamic equations in the slow-motion approximation to general relativity. Part II. Radiation reaction and higher-order divergent terms”, Gen. Relativ. Gravit., 12, 521-543 (1980). [DOI]. (Cited on pages 53 and 57.) · doi:10.1007/BF00756528
[271] Kidder, L. E., “Coalescing binary systems of compact objects to (post)5/2-Newtonian order. V. Spin effects”, Phys. Rev. D, 52, 821-847 (1995). [DOI], [ADS]. (Cited on pages 19, 21, 22, 102, 147, 150, and 152.) · doi:10.1103/PhysRevD.52.821
[272] Kidder, L. E., “Using full information when computing modes of post-Newtonian waveforms from inspiralling compact binaries in circular orbits”, Phys. Rev. D, 77, 044016 (2008). [DOI], [arXiv:0710.0614]. (Cited on pages 20, 36, 37, 131, and 134.) · doi:10.1103/PhysRevD.77.044016
[273] Kidder, L. E., Blanchet, L. and Iyer, B. R., “A note on the radiation reaction in the 2.5PN waveform from inspiralling binaries in quasi-circular orbits”, Class. Quantum Grav., 24, 5307 (2007). [DOI], [arXiv:0706.0726]. (Cited on page 20.) · Zbl 1126.83006 · doi:10.1088/0264-9381/24/20/N01
[274] Kidder, L. E., Will, C. M. and Wiseman, A. G., “Coalescing binary systems of compact objects to (post)5/2-Newtonian order. III. Transition from inspiral to plunge”, Phys. Rev. D, 47, 3281-3291 (1993). [DOI], [ADS]. (Cited on page 103.) · doi:10.1103/PhysRevD.47.3281
[275] Kidder, L. E., Will, C. M. and Wiseman, A. G., “Spin effects in the inspiral of coalescing compact binaries”, Phys. Rev. D, 47, R4183-R4187 (1993). [DOI]. (Cited on pages 19, 21, 102, 104, 105, and 147.) · doi:10.1103/PhysRevD.47.R4183
[276] Kochanek, C. S., “Coalescing binary neutron stars”, Astrophys. J., 398, 234-247 (1992). [DOI], [ADS]. (Cited on page 15.) · doi:10.1086/171851
[277] Kol, B. and Smolkin, M., “Non-relativistic gravitation: From Newton to Einstein and back”, Class. Quantum Grav., 25, 145011 (2008). [DOI], [arXiv:0712.4116 [hep-th]]. (Cited on page 18.) · Zbl 1180.83019 · doi:10.1088/0264-9381/25/14/145011
[278] Königsdörffer, C., Faye, G. and Schäfer, G., “The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism”, Phys. Rev. D, 68, 044004 (2003). [DOI], [astro-ph/0305048]. (Cited on pages 18, 78, 92, and 117.) · doi:10.1103/PhysRevD.68.044004
[279] Königsdörffer, C. and Gopakumar, A., “Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order”, Phys. Rev. D, 73, 124012 (2006). [DOI], [ADS], [gr-qc/0603056]. (Cited on page 146.) · doi:10.1103/PhysRevD.73.124012
[280] Kopeikin, S. M., “The equations of motion of extended bodies in general-relativity with conservative corrections and radiation damping taken into account”, Astron. Zh., 62, 889-904 (1985). (Cited on pages 17 and 70.)
[281] Kopeikin, S. M., “Celestial Coordinate Reference Systems in Curved Spacetime”, Celest. Mech., 44, 87 (1988). [DOI]. (Cited on page 70.) · Zbl 0678.70020 · doi:10.1007/BF01230709
[282] Kopeikin, S. M., Schäfer, G., Gwinn, C. R. and Eubanks, T. M., “Astrometric and timing effects of gravitational waves from localized sources”, Phys. Rev. D, 59, 084023 (1999). [DOI], [ADS], [gr-qc/9811003]. (Cited on page 12.) · doi:10.1103/PhysRevD.59.084023
[283] Kozai, Y., “Secular perturbations of asteroids with high inclination and eccentricity”, Astron. J., 67, 591-598 (1962). [DOI], [ADS]. (Cited on pages 15 and 135.) · doi:10.1086/108790
[284] Królak, A., Kokkotas, K. D. and Schäfer, G., “Estimation of the post-Newtonian parameters in the gravitational-wave emission of a coalescing binary”, Phys. Rev. D, 52, 2089-2111 (1995). [DOI], [gr-qc/9503013]. (Cited on pages 16, 65, and 124.) · doi:10.1103/PhysRevD.52.2089
[285] Landau, L. D. and Lifshitz, E. M., The classical theory of fields, (Pergamon Press, Oxford; New York, 1971), 3rd edition. (Cited on pages 9, 12, and 121.) · Zbl 0178.28704
[286] Le Tiec, A., “First law of mechanics for compact binaries on eccentric orbits”, Phys. Rev. D, 92, 084021 (2015). [DOI], [arXiv:1506.05648 [gr-qc]]. (Cited on page 111.) · doi:10.1103/PhysRevD.92.084021
[287] Le Tiec, A., Barausse, E. and Buonanno, A., “Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems”, Phys. Rev. Lett., 108, 131103 (2012). [DOI], [arXiv:1111.5609 [gr-qc]]. (Cited on pages 96 and 108.) · doi:10.1103/PhysRevLett.108.131103
[288] Le Tiec, A. and Blanchet, L., “The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions”, Class. Quantum Grav., 27, 045008 (2010). [DOI], [arXiv:0901.4593 [gr-qc]]. (Cited on page 22.) · Zbl 1186.83017 · doi:10.1088/0264-9381/27/4/045008
[289] Le Tiec, A., Blanchet, L. and Whiting, B. F., “First law of binary black hole mechanics in general relativity and post-Newtonian theory”, Phys. Rev. D, 85, 064039 (2012). [DOI], [arXiv:1111.5378 [gr-qc]]. (Cited on pages 95, 96, 108, 110, 113, and 114.) · doi:10.1103/PhysRevD.85.064039
[290] Le Tiec, A., Blanchet, L. and Will, C. M., “Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries”, Class. Quantum Grav., 27, 012001 (2010). [DOI], [arXiv:0901.4594 [gr-qc]]. (Cited on page 22.) · Zbl 1184.83030 · doi:10.1088/0264-9381/27/1/012001
[291] Le Tiec, A., Mroué, A. H., Barack, L., Buonanno, A., Pfeiffer, H. P., Sago, N. and Taracchini, A., “Periastron Advance in Black-Hole Binaries”, Phys. Rev. Lett., 107, 141101 (2011). [arXiv:1106.3278 [gr-qc]]. (Cited on page 140.) · doi:10.1103/PhysRevLett.107.141101
[292] Levi, M., “Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach”, Phys. Rev. D, 82, 104004 (2010). [DOI], [arXiv:1006.4139 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.82.104004
[293] Levi, M., “Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction”, Phys. Rev. D, 82, 064029 (2010). [DOI], [ADS], [arXiv:0802.1508 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.82.064029
[294] Levi, M., “Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order”, Phys. Rev. D, 85, 064043 (2012). [DOI], [ADS], [arXiv:1107.4322]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.85.064043
[295] Levi, M. and Steinhoff, J., “Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals”, J. Cosmol. Astropart. Phys., 2014(12), 003 (2014). [DOI], [arXiv:1408.5762 [gr-qc]]. (Cited on page 19.) · doi:10.1088/1475-7516/2014/12/003
[296] Levi, M. and Steinhoff, J., “Leading order finite size effects with spins for inspiralling compact binaries”, J. High Energy Phys., 2015(06), 059 (2015). [DOI], [arXiv:1410.2601 [gr-qc]]. (Cited on page 147.) · doi:10.1007/JHEP06(2015)059
[297] Levi, M. and Steinhoff, J., “Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme”, arXiv, e-print, (2015). [arXiv:1506.05056 [gr-qc]]. (Cited on pages 19 and 147.)
[298] Levi, M. and Steinhoff, J., “Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme”, arXiv, e-print, (2015). [arXiv:1506.05794 [gr-qc]]. (Cited on pages 19 and 147.)
[299] Levi, M. and Steinhoff, J., “Spinning gravitating objects in the effective field theory in the post-Newtonian scheme”, J. High Energy Phys., 2015(09), 219 (2015). [DOI], [arXiv:1501.04956 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1388.83031 · doi:10.1007/JHEP09(2015)219
[300] Lidov, M. L., “The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies”, Planet. Space Sci., 9, 719 (1962). [DOI]. (Cited on pages 15 and 135.) · doi:10.1016/0032-0633(62)90129-0
[301] Limousin, F., Gondek-Rosinska, D. and Gourgoulhon, E., “Last orbits of binary strange quark stars”, Phys. Rev. D, 71, 064012 (2005). [DOI], [ADS], [arXiv:gr-qc/0411127 [gr-qc]]. (Cited on page 101.) · doi:10.1103/PhysRevD.71.064012
[302] Lincoln, C. W. and Will, C. M., “Coalescing binary systems of compact objects to (post)5/2-Newtonian order: Late-time evolution and gravitational-radiation emission”, Phys. Rev. D, 42, 1123-1143 (1990). [DOI], [ADS]. (Cited on page 92.) · doi:10.1103/PhysRevD.42.1123
[303] Lorentz, HA; Droste, J., The motion of a system of bodies under the influence of their mutual attraction, according to Einstein’s theory“, 330-355 (1937), The Hague · doi:10.1007/978-94-015-3445-1_11
[304] Madore, J., “Gravitational radiation from a bounded source. I”, Ann. Inst. Henri Poincare, 12, 285-305 (1970). Online version (accessed 6 October 2013): http://www.numdam.org/item?id=AIHPA_1970__12_3_285_0. (Cited on pages 33 and 34.)
[305] Marsat, S., “Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries”, Class. Quantum Grav., 32, 085008 (2015). [DOI], [arXiv:1411.4118 [gr-qc]]. (Cited on page 147.) · Zbl 1328.83103 · doi:10.1088/0264-9381/32/8/085008
[306] Marsat, S., Bohé, A., Blanchet, L. and Buonanno, A., “Next-to-leading tail-induced spin-orbit effects in the gravitational radiation of compact binaries”, Class. Quantum Grav., 31, 025023 (2013). [DOI], [arXiv:1307.6793 [gr-qc]]. (Cited on pages 21, 147, 154, and 158.) · Zbl 1292.83020 · doi:10.1088/0264-9381/31/2/025023
[307] Marsat, S., Bohé, A., Faye, G. and Blanchet, L., “Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems”, Class. Quantum Grav., 30, 055007 (2013). [DOI], [arXiv:1210.4143]. (Cited on pages 19, 147, 153, and 158.) · Zbl 1263.83038 · doi:10.1088/0264-9381/30/5/055007
[308] Martin, J. and Sanz, J. L., “Slow motion approximation in predictive relativistic mechanics. II. Non-interaction theorem for interactions derived from the classical field-theory”, J. Math. Phys., 20, 25-34 (1979). [DOI]. (Cited on page 85.) · doi:10.1063/1.523958
[309] Mathews, J., “Gravitational multipole radiation”, J. Soc. Ind. Appl. Math., 10, 768-780 (1962). [DOI]. (Cited on page 10.) · Zbl 0114.21201 · doi:10.1137/0110059
[310] Mathisson, M., “Republication of: New mechanics of material systems”, Gen. Relativ. Gravit., 42, 1011-1048 (2010). [DOI]. (Cited on pages 148 and 150.) · Zbl 1188.83018 · doi:10.1007/s10714-010-0939-y
[311] McClintock, J. E., Shafee, R., Narayan, R., Remillard, R. A., Davis, S. W. and Li, L.-X., “The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105”, Astrophys. J., 652, 518-539 (2006). [DOI], [ADS], [arXiv:astro-ph/0606076]. (Cited on page 146.) · doi:10.1086/508457
[312] Memmesheimer, R., Gopakumar, A. and Schäafer, G., “Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits”, Phys. Rev. D, 70, 104011 (2004). [DOI], [gr-qc/0407049]. (Cited on pages 135, 138, 140, and 141.) · doi:10.1103/PhysRevD.70.104011
[313] Merritt, D., Milosavljević, M., Favata, M., Hughes, S. A. and Holz, D. E., “Consequences of Gravitational Radiation Recoil”, Astrophys. J. Lett., 607, L9-L12 (2004). [DOI], [ADS], [astro-ph/0402057]. (Cited on page 21.) · Zbl 1118.85319 · doi:10.1086/421551
[314] Mikóczi, B., Vasúth, M. and Gergely, L.Á., “Self-interaction spin effects in inspiralling compact binaries”, Phys. Rev. D, 71, 124043 (2005). [DOI], [astro-ph/0504538]. (Cited on pages 21 and 147.) · doi:10.1103/PhysRevD.71.124043
[315] Miller, M. C. and Hamilton, D. P., “Four-Body Effects in Globular Cluster Black Hole Coalescence”, Astrophys. J., 576, 894 (2002). [DOI], [astro-ph/0202298]. (Cited on page 15.) · doi:10.1086/341788
[316] Mino, Y., Sasaki, M., Shibata, M., Tagoshi, H. and Tanaka, T., “Black Hole Perturbation”, Prog. Theor. Phys. Suppl., 128, 1-121 (1997). [DOI], [gr-qc/9712057]. (Cited on page 21.) · Zbl 0985.83510 · doi:10.1143/PTPS.128.1
[317] Mino, Y., Sasaki, M. and Tanaka, T., “Gravitational radiation reaction to a particle motion”, Phys. Rev. D, 55, 3457-3476 (1997). [DOI], [arXiv:gr-qc/9606018]. (Cited on page 112.) · Zbl 1128.90360 · doi:10.1103/PhysRevD.55.3457
[318] Mirshekari, S. and Will, C. M., “Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order”, Phys. Rev. D, 87, 084070 (2013). [DOI], [ADS], [arXiv:1301.4680 [gr-qc]]. (Cited on page 17.) · doi:10.1103/PhysRevD.87.084070
[319] Misner, C. W., Thorne, K. S. and Wheeler, J. A., Gravitation, (W. H. Freeman, San Francisco, 1973). [ADS]. (Cited on pages 13, 14, and 150.)
[320] Mora, T. and Will, C. M., “Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects”, Phys. Rev. D, 69, 104021 (2004). [DOI], [arXiv:gr-qc/0312082]. (Cited on pages 16, 92, and 93.) · doi:10.1103/PhysRevD.69.104021
[321] Moritz, H., Advanced Physical Geodesy, (H. Wichmann, Karlsruhe, 1980). (Cited on page 15.)
[322] Nissanke, S. and Blanchet, L., “Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order”, Class. Quantum Grav., 22, 1007-1031 (2005). [DOI], [gr-qc/0412018]. (Cited on pages 18, 78, 92, and 117.) · Zbl 1073.83021 · doi:10.1088/0264-9381/22/6/008
[323] Nowak, MA; Wilms, J.; Pottschmidt, K.; Schulz, N.; Miller, J.; Maitra, D.; Petre, R. (ed.); Mitsuda, K. (ed.); Angelini, L. (ed.), Suzaku observations of 4U 1957+11: The most rapidly spinning black hole in the galaxy?, No. 1427, 48-51 (2012), Melville, NY
[324] Ohta, T., Okamura, H., Kimura, T. and Hiida, K., “Physically acceptable solution of Einstein’s equation for many-body system”, Prog. Theor. Phys., 50, 492-514 (1973). [DOI]. (Cited on pages 17, 18, and 97.) · doi:10.1143/PTP.50.492
[325] Ohta, T., Okamura, H., Kimura, T. and Hiida, K., “Coordinate Condition and Higher Order Gravitational Potential in Canocical Formalism”, Prog. Theor. Phys., 51, 1598-1612 (1974). [DOI]. (Cited on pages 17 and 18.) · doi:10.1143/PTP.51.1598
[326] Ohta, T., Okamura, H., Kimura, T. and Hiida, K., “Higher-order gravitational potential for many-body system”, Prog. Theor. Phys., 51, 1220-1238 (1974). [DOI]. (Cited on pages 17 and 18.) · doi:10.1143/PTP.51.1220
[327] Okamura, H., Ohta, T., Kimura, T. and Hiida, K., “Perturbation calculation of gravitational potentials”, Prog. Theor. Phys., 50, 2066-2079 (1973). [DOI]. (Cited on pages 17 and 18.) · doi:10.1143/PTP.50.2066
[328] Owen, B. J., Tagoshi, H. and Ohashi, A., “Nonprecessional spin-orbit effects on gravitational waves from inspiraling compact binaries to second post-Newtonian order”, Phys. Rev. D, 57, 6168-6175 (1998). [DOI], [gr-qc/9710134]. (Cited on page 21.) · doi:10.1103/PhysRevD.57.6168
[329] Pan, Y., Buonanno, A., Buchman, L. T., Chu, T., Kidder, L. E., Pfeiffer, H. P. and Scheel, M. A., “Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of non-precessing, spinning, equal-mass black holes”, Phys. Rev. D, 81, 084041 (2010). [DOI], [ADS], [arXiv:0912.3466 [gr-qc]]. (Cited on page 65.) · doi:10.1103/PhysRevD.81.084041
[330] Papapetrou, A., “Equations of motion in general relativity”, Proc. Phys. Soc. London, Sect. B, 64, 57-75 (1951). (Cited on page 17.) · Zbl 0044.42104 · doi:10.1088/0370-1298/64/1/310
[331] Papapetrou, A., “Spinning Test-Particles in General Relativity. I”, Proc. R. Soc. London, Ser. A, 209, 248-258 (1951). [DOI]. (Cited on pages 148 and 150.) · Zbl 0044.22801 · doi:10.1098/rspa.1951.0200
[332] Papapetrou, A., “Relativité — une formule pour le rayonnement gravitationnel en première approximation”, C. R. Acad. Sci. Ser. II, 255, 1578 (1962). (Cited on page 10.) · Zbl 0100.40504
[333] Papapetrou, A., “Étude systématique du rayonnement gravitationnel 4-polaire. Énergie-impulsion et moment cinétique du rayonnement”, Ann. Inst. Henri Poincare, XIV, 79 (1971). (Cited on page 10.)
[334] Papapetrou, A. and Linet, B., “Equation of motion including the reaction of gravitational radiation”, Gen. Relativ. Gravit., 13, 335 (1981). [DOI]. (Cited on pages 53 and 57.) · Zbl 0477.76129 · doi:10.1007/BF01025468
[335] Pati, M. E. and Will, C. M., “Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations: Foundations”, Phys. Rev. D, 62, 124015 (2000). [DOI], [gr-qc/0007087]. (Cited on pages 11 and 50.) · doi:10.1103/PhysRevD.62.124015
[336] Pati, M. E. and Will, C. M., “Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. II. Two-body equations of motion to second post-Newtonian order, and radiation reaction to 3.5 post-Newtonian order”, Phys. Rev. D, 65, 104008 (2002). [DOI], [ADS], [gr-qc/0201001]. (Cited on pages 11, 18, 78, 92, and 117.) · doi:10.1103/PhysRevD.65.104008
[337] Penrose, R., “Asymptotic Properties of Fields and Space-Times”, Phys. Rev. Lett., 10, 66-68 (1963). [DOI], [ADS]. (Cited on pages 10, 11, 33, and 34.) · doi:10.1103/PhysRevLett.10.66
[338] Penrose, R., “Zero Rest-Mass Fields Including Gravitation: Asymptotic Behaviour”, Proc. R. Soc. London, Ser. A, 284, 159-203 (1965). [DOI], [ADS]. (Cited on pages 10, 11, 33, and 34.) · Zbl 0129.41202 · doi:10.1098/rspa.1965.0058
[339] Peters, P. C., “Gravitational Radiation and the Motion of Two Point Masses”, Phys. Rev., 136, B1224-B1232 (1964). [DOI], [ADS]. (Cited on pages 10, 13, 14, 135, 140, and 145.) · Zbl 0129.41201 · doi:10.1103/PhysRev.136.B1224
[340] Peters, P. C. and Mathews, J., “Gravitational Radiation from Point Masses in a Keplerian Orbit”, Phys. Rev., 131, 435-440 (1963). [DOI], [ADS]. (Cited on pages 13, 14, 135, 140, and 143.) · Zbl 0114.43902 · doi:10.1103/PhysRev.131.435
[341] Petrova, N. M., “Ob Uravnenii Dvizheniya i Tenzore Materii dlya Sistemy Konechnykh Mass v Obshchei Teorii Otnositielnosti”, J. Exp. Theor. Phys., 19(11), 989-999 (1949). (Cited on page 17.)
[342] Pfeiffer, H. P., Teukolsky, S. A. and Cook, G. B., “Quasicircular orbits for spinning binary black holes”, Phys. Rev. D, 62, 104018 (2000). [DOI], [ADS], [gr-qc/0006084]. (Cited on pages 103 and 104.) · doi:10.1103/PhysRevD.62.104018
[343] Pirani, FAE; Trautman, A. (ed.); Pirani, FAE (ed.); Bondi, H. (ed.), Introduction to Gravitational Radiation Theory, No. 1964, 249-373 (1965), Englewood Cliffs, NJ
[344] Plebański, J. F. and Bażański, S. L., “The general Fokker action principle and its application in general relativity theory”, Acta Phys. Pol., 18, 307-345 (1959). (Cited on page 53.) · Zbl 0087.42602
[345] Poisson, E., “Gravitational radiation from a particle in circular orbit around a black hole. I. Analytic results for the nonrotating case”, Phys. Rev. D, 47, 1497-1510 (1993). [DOI], [ADS]. (Cited on pages 21 and 38.) · doi:10.1103/PhysRevD.47.1497
[346] Poisson, E., “Gravitational radiation from a particle in circular orbit around a black-hole. VI. Accuracy of the post-Newtonian expansion”, Phys. Rev. D, 52, 5719-5723 (1995). [DOI], [gr-qc/9505030]. Erratum: Phys. Rev. D, 55, 7980 (1997). (Cited on pages 16, 65, and 125.) · doi:10.1103/PhysRevD.52.5719
[347] Poisson, E., “Gravitational waves from inspiraling compact binaries: The quadrupole-moment term”, Phys. Rev. D, 57, 5287-5290 (1997). [DOI], [gr-qc/9709032]. (Cited on page 147.) · doi:10.1103/PhysRevD.57.5287
[348] Poisson, E., Pound, A. and Vega, I., “The Motion of Point Particles in Curved Spacetime”, Living Rev. Relativity, 14, lrr-2011-7 (2011). [DOI], [ADS], [arXiv:1102.0529 [gr-qc]]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2011-7. (Cited on pages 9 and 112.) · Zbl 1316.83024
[349] Poisson, E. and Sasaki, M., “Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections”, Phys. Rev. D, 51, 5753-5767 (1995). [DOI], [gr-qc/9412027]. (Cited on pages 123 and 158.) · doi:10.1103/PhysRevD.51.5753
[350] Poisson, E. and Will, C. M., “Gravitational waves from inspiraling compact binaries: Parameter estimation using second-post-Newtonian wave forms”, Phys. Rev. D, 52, 848-855 (1995). [DOI], [arXiv:gr-qc/9502040]. (Cited on pages 16, 65, and 124.) · doi:10.1103/PhysRevD.52.848
[351] Porto, R. A., “Post-Newtonian corrections to the motion of spinning bodies in NRGR”, Phys. Rev. D, 73, 104031 (2006). [DOI], [gr-qc/0511061]. (Cited on pages 147 and 148.) · doi:10.1103/PhysRevD.73.104031
[352] Porto, R. A., “Next-to-leading-order spin-orbit effects in the motion of inspiralling compact binaries”, Class. Quantum Grav., 27, 205001 (2010). [DOI], [arXiv:1005.5730 [gr-qc]]. (Cited on pages 19 and 147.) · Zbl 1202.83019 · doi:10.1088/0264-9381/27/20/205001
[353] Porto, R. A., Ross, A. and Rothstein, I. Z., “Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order”, J. Cosmol. Astropart. Phys., 2011(3), 009 (2011). [DOI], [arXiv:1007.1312 [gr-qc]]. (Cited on page 21.) · doi:10.1088/1475-7516/2011/03/009
[354] Porto, R. A. and Rothstein, I. Z., “Calculation of the first nonlinear contribution to the general-relativistic spin-spin interaction for binary systems”, Phys. Rev. Lett., 97, 021101 (2006). [DOI], [arXiv:gr-qc/0604099]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevLett.97.021101
[355] Porto, R. A. and Rothstein, I. Z., “Next to leading order spin(1)spin(1) effects in the motion of inspiralling compact binaries”, Phys. Rev. D, 78, 044013 (2008). [DOI], [ADS], [arXiv:0804.0260 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.78.044013
[356] Porto, R. A. and Rothstein, I. Z., “Spin(1)spin(2) effects in the motion of inspiralling compact binaries at third order in the post-Newtonian expansion”, Phys. Rev. D, 78, 044012 (2008). [DOI], [arXiv:0802.0720 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.78.044012
[357] Poujade, O. and Blanchet, L., “Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions”, Phys. Rev. D, 65, 124020 (2002). [DOI], [gr-qc/0112057]. (Cited on pages 11, 54, 55, 56, 57, and 59.) · doi:10.1103/PhysRevD.65.124020
[358] Press, W. H., “Gravitational Radiation from Sources Which Extend Into Their Own Wave Zone”, Phys. Rev. D, 15, 965-968 (1977). [DOI]. (Cited on page 10.) · doi:10.1103/PhysRevD.15.965
[359] Pretorius, F., “Evolution of Binary Black-Hole Spacetimes”, Phys. Rev. Lett., 95, 121101 (2005). [DOI], [ADS], [arXiv:gr-qc/0507014]. (Cited on page 8.) · doi:10.1103/PhysRevLett.95.121101
[360] Quinn, T. C. and Wald, R. M., “Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime”, Phys. Rev. D, 56, 3381-3394 (1997). [DOI], [arXiv:gr-qc/9610053]. (Cited on page 112.) · doi:10.1103/PhysRevD.56.3381
[361] Rendall, A. D., “Convergent and divergent perturbation series and the post-Minkowskian scheme”, Class. Quantum Grav., 7, 803 (1990). [DOI]. (Cited on pages 9 and 28.) · Zbl 0701.35148 · doi:10.1088/0264-9381/7/5/010
[362] Rendall, A. D., “On the definition of post-Newtonian approximations”, Proc. R. Soc. London, Ser. A, 438, 341-360 (1992). [DOI]. (Cited on pages 9, 28, and 54.) · Zbl 0754.53062 · doi:10.1098/rspa.1992.0111
[363] Rendall, A. D., “The Newtonian limit for asymptotically flat solutions of the Einstein-Vlasov system”, Commun. Math. Phys., 163, 89-112 (1994). [DOI], [gr-qc/9303027]. (Cited on pages 9 and 28.) · Zbl 0816.53058 · doi:10.1007/BF02101736
[364] Reynolds, C. S., “Measuring Black Hole Spin Using X-Ray Reflection Spectroscopy”, Space Sci. Rev., 183, 277-294 (2014). [DOI], [ADS], [arXiv:1302.3260 [astro-ph.HE]]. (Cited on page 146.) · doi:10.1007/s11214-013-0006-6
[365] Riesz, M., “L’intégrale de Riemann-Liouville et le problème de Cauchy”, Acta Math., 81, 1-218 (1949). [DOI]. (Cited on page 67.) · Zbl 0033.27601 · doi:10.1007/BF02395016
[366] Rieth, R. and Schäfer, G., “Spin and tail effects in the gravitational-wave emission of compact binaries”, Class. Quantum Grav., 14, 2357 (1997). [DOI]. (Cited on pages 140 and 145.) · Zbl 0875.83046 · doi:10.1088/0264-9381/14/8/029
[367] Sachs, R. K., “Gravitational waves in general relativity. VI. The outgoing radiation condition”, Proc. R. Soc. London, Ser. A, 264, 309-338 (1961). [DOI]. (Cited on page 10.) · Zbl 0098.19204 · doi:10.1098/rspa.1961.0202
[368] Sachs, R. K., “Gravitational Waves in General Relativity. VIII. Waves in Asymptotically Flat Space-Time”, Proc. R. Soc. London, Ser. A, 270, 103-126 (1962). [DOI], [ADS]. (Cited on pages 10, 11, and 33.) · Zbl 0101.43605 · doi:10.1098/rspa.1962.0206
[369] Sachs, R. K. and Bergmann, P. G., “Structure of Particles in Linearized Gravitational Theory”, Phys. Rev., 112, 674-680 (1958). [DOI]. (Cited on page 10.) · Zbl 0083.43001 · doi:10.1103/PhysRev.112.674
[370] Sago, N., Barack, L. and Detweiler, S., “Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results”, Phys. Rev. D, 78, 124024 (2008). [DOI], [arXiv:0810.2530]. (Cited on page 109.) · doi:10.1103/PhysRevD.78.124024
[371] Santamaría, L. et al., “Matching post-Newtonian and numerical relativity waveforms: Systematic errors and a new phenomenological model for non-precessing black hole binaries”, Phys. Rev. D, 82, 064016 (2010). [DOI], [ADS], [arXiv:1005.3306 [gr-qc]]. (Cited on page 65.) · doi:10.1103/PhysRevD.82.064016
[372] Sasaki, M., “Post-Newtonian Expansion of the Ingoing-Wave Regge-Wheeler Function”, Prog. Theor. Phys., 92, 17-36 (1994). [DOI]. (Cited on page 21.) · doi:10.1143/ptp/92.1.17
[373] Sasaki, M. and Tagoshi, H., “Analytic Black Hole Perturbation Approach to Gravitational Radiation”, Living Rev. Relativity, 6, lrr-2003-6 (2003). [DOI], [ADS], [arXiv:gr-qc/0306120]. URL (accessed 6 October 2013): http://www.livingreviews.org/lrr-2003-6. (Cited on page 9.) · Zbl 1070.83019
[374] Schäafer, G., “Acceleration-dependent Lagrangians in general relativity”, Phys. Lett. A, 100, 128 (1984). [DOI]. (Cited on page 62.) · doi:10.1016/0375-9601(84)90947-2
[375] Schäafer, G., “The Gravitational Quadrupole Radiation-Reaction Force and the Canonical Formalism of ADM”, Ann. Phys. (N.Y.), 161, 81-100 (1985). [DOI]. (Cited on page 17.) · doi:10.1016/0003-4916(85)90337-9
[376] Schäafer, G., “The ADM Hamiltonian at the Postlinear Approximation”, Gen. Relativ. Gravit., 18, 255-270 (1986). [DOI]. (Cited on page 17.) · doi:10.1007/BF00765886
[377] Schäfer, G., “Three-body Hamiltonian in general relativity”, Phys. Lett., 123, 336-339 (1987). [DOI]. (Cited on page 97.) · doi:10.1016/0375-9601(87)90389-6
[378] Schäafer, G.; Blanchet, L. (ed.); Spallicci, A. (ed.); Whiting, B. (ed.), Post-Newtonian Methods: Analytic Results on the Binary Problem, Lectures from the CNRS School on Mass, Orléans, France, 23-25 June 2008, Dordrecht; New York · Zbl 1213.83043
[379] Schäafer, G. and Wex, N., “Second post-Newtonian motion of compact binaries”, Phys. Lett. A, 174, 196-205 (1993). [DOI]. Erratum: Phys. Lett. A, 177, 461 (1993). (Cited on pages 138 and 141.) · doi:10.1016/0375-9601(93)90758-R
[380] Schwartz, L., “Sur l’impossibilite de la multiplication des distributions”, C. R. Acad. Sci. Ser. II, 239, 847-848 (1954). (Cited on pages 68 and 69.) · Zbl 0056.10602
[381] Schwartz, L., Théorie des distributions, (Hermann, Paris, 1978). (Cited on pages 66, 67, and 75.) · Zbl 0399.46028
[382] Sellier, A., “Hadamard’s finite part concept in dimension <Emphasis Type=”Italic“>n ≥ 2, distributional definition, regularization forms and distributional derivatives”, Proc. R. Soc. London, Ser. A, 445, 69-98 (1994). [DOI]. (Cited on page 66.) · Zbl 0815.46034 · doi:10.1098/rspa.1994.0049
[383] Shah, A., Friedmann, J. and Whiting, B. F., “Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation”, Phys. Rev. D, 89, 064042 (2014). [DOI], [arXiv:1312.1952 [gr-qc]]. (Cited on page 116.) · doi:10.1103/PhysRevD.89.064042
[384] Simon, W. and Beig, R., “The multipole structure of stationary space-times”, J. Math. Phys., 24, 1163-1171 (1983). [DOI]. (Cited on page 10.) · Zbl 0515.53025 · doi:10.1063/1.525846
[385] Sopuerta, C. F., Yunes, N. and Laguna, P., “Gravitational Recoil from Binary Black Hole Mergers: the Close-Limit Approximation”, Phys. Rev. D, 74, 124010 (2006). [DOI], [astro-ph/0608600]. (Cited on page 22.) · doi:10.1103/PhysRevD.74.124010
[386] Steinhoff, J., “Canonical formulation of spin in general relativity”, Ann. Phys. (Berlin), 523, 296 (2011). [DOI], [arXiv:1106.4203 [gr-qc]]. (Cited on page 148.) · Zbl 1218.83018 · doi:10.1002/andp.201000178
[387] Steinhoff, J., Hergt, S. and Schäfer, G., “Next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form”, Phys. Rev. D, 77, 081501(R) (2008). [arXiv:0712.1716 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.77.081501
[388] Steinhoff, J., Hergt, S. and Schäfer, G., “Spin-squared Hamiltonian of next-to-leading order gravitational interaction”, Phys. Rev. D, 78, 101503(R) (2008). [arXiv:0809.2200 [gr-qc]]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.78.101503
[389] Steinhoff, J., Schäfer, G. and Hergt, S., “ADM canonical formalism for gravitating spinning objects”, Phys. Rev. D, 77, 104018 (2008). [DOI], [arXiv:0805.3136 [gr-qc]]. (Cited on pages 19, 147, and 148.) · doi:10.1103/PhysRevD.77.104018
[390] Strohmayer, T. E., “Discovery of a 450 Hz quasi-periodic oscillation from the microquasar GRO J1655-40 with the Rossi X-ray Timing Explorer”, Astrophys. J. Lett., 552, L49-L53 (2001). [DOI], [ADS]. (Cited on page 146.) · doi:10.1086/320258
[391] ’t Hooft, G. and Veltman, M., “Regularization and renormalization of gauge fields”, Nucl. Phys. B, 44, 139 (1972). [DOI]. (Cited on page 72.) · doi:10.1016/0550-3213(72)90279-9
[392] Tagoshi, H., Mano, S. and Takasugi, E., “Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole”, Prog. Theor. Phys., 98, 829 (1997). [DOI], [gr-qc/9711072]. (Cited on pages 123 and 158.) · doi:10.1143/PTP.98.829
[393] Tagoshi, H. and Nakamura, T., “Gravitational waves from a point particle in circular orbit around a black hole: Logarithmic terms in the post-Newtonian expansion”, Phys. Rev. D, 49, 4016-4022 (1994). [DOI]. (Cited on pages 16, 21, 65, and 123.) · doi:10.1103/PhysRevD.49.4016
[394] Tagoshi, H., Ohashi, A. and Owen, B. J., “Gravitational field and equations of motion of spinning compact binaries to 2.5-post-Newtonian order”, Phys. Rev. D, 63, 044006 (2001). [DOI], [gr-qc/0010014]. (Cited on pages 19 and 147.) · doi:10.1103/PhysRevD.63.044006
[395] Tagoshi, H. and Sasaki, M., “Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbit around a Schwarzschild Black Hole”, Prog. Theor. Phys., 92, 745-771 (1994). [DOI], [gr-qc/9405062]. (Cited on pages 21 and 123.) · doi:10.1143/ptp/92.4.745
[396] Tagoshi, H., Shibata, M., Tanaka, T. and Sasaki, M., “Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a rotating black hole: Up to <Emphasis Type=”Italic“>O(<Emphasis Type=”Italic“>v8) beyond the quadrupole formula”, Phys. Rev. D, 54, 1439-1459 (1996). [DOI]. (Cited on page 158.) · doi:10.1103/PhysRevD.54.1439
[397] Tanaka, T., Tagoshi, H. and Sasaki, M., “Gravitational Waves by a Particle in Circular Orbit around a Schwarzschild Black Hole: 5.5 Post-Newtonian Formula”, Prog. Theor. Phys., 96, 1087-1101 (1996). [DOI], [gr-qc/9701050]. (Cited on pages 21 and 123.) · doi:10.1143/PTP.96.1087
[398] Taylor, J. H., “Pulsar timing and relativistic gravity”, Class. Quantum Grav., 10, 167-174 (1993). [DOI]. (Cited on pages 7, 13, and 14.) · doi:10.1088/0264-9381/10/S/017
[399] Taylor, J. H., Fowler, L. A. and McCulloch, P. M., “Measurements of general relativistic effects in the binary pulsar PSR 1913+16”, Nature, 277, 437-440 (1979). [DOI]. (Cited on pages 7, 13, and 14.) · doi:10.1038/277437a0
[400] Taylor, J. H. and Weisberg, J. M., “A New Test of General Relativity: Gravitational Radiation and the Binary Pulsar PSR 1913+16”, Astrophys. J., 253, 908-920 (1982). [DOI]. (Cited on pages 7, 13, and 14.) · doi:10.1086/159690
[401] Tessmer, M. and Schäfer, G., “Full-analytic frequency-domain 1PN-accurate gravitational wave forms from eccentric compact binaries”, Phys. Rev. D, 82, 124064 (2010). [DOI], [arXiv:1006.3714 [gr-qc]]. (Cited on page 141.) · doi:10.1103/PhysRevD.82.124064
[402] Tessmer, M. and Schäfer, G., “Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy”, Ann. Phys. (Berlin), 523, 813 (2011). [DOI], [arXiv:1012.3894 [gr-qc]]. (Cited on page 141.) · Zbl 1229.83033 · doi:10.1002/andp.201100007
[403] Thorne, K. S., “Multipole expansions of gravitational radiation”, Rev. Mod. Phys., 52, 299-339 (1980). [DOI], [ADS]. (Cited on pages 10, 11, 20, 26, 27, 35, 36, 37, and 50.) · doi:10.1103/RevModPhys.52.299
[404] Thorne, KS; Deruelle, N. (ed.); Piran, T. (ed.), The theory of gravitational radiation: An introductory review, NATO Advanced Study Institute, Centre de physique des Houches, 2-21 June 1982, Amsterdam; New York
[405] Thorne, KS; Hawking, SW (ed.); Israel, W. (ed.), Gravitational radiation, 330-458 (1987), Cambridge; New York · Zbl 0966.83515
[406] Thorne, K. S., “Gravitational-wave bursts with memory: The Christodoulou effect”, Phys. Rev. D, 45, 520 (1992). [DOI]. (Cited on pages 21 and 43.) · doi:10.1103/PhysRevD.45.520
[407] Thorne, K. S. and Hartle, J. B., “Laws of motion and precession for black holes and other bodies”, Phys. Rev. D, 31, 1815-1837 (1985). [DOI]. (Cited on page 70.) · doi:10.1103/PhysRevD.31.1815
[408] Thorne, K. S. and Kovacs, S. J., “Generation of gravitational waves. I. Weak-field sources”, Astrophys. J., 200, 245-262 (1975). [DOI]. (Cited on page 10.) · doi:10.1086/153783
[409] Trautman, A., “Lectures on General Relativity”, Gen. Relativ. Gravit., 34, 721-762 (2002). [DOI]. Lectures delivered at King’s College in London in May-June 1958. (Cited on pages 148 and 150.) · Zbl 1004.83001 · doi:10.1023/A:1015939926662
[410] Trias, M. and Sintes, A. M., “LISA observations of supermassive black holes: Parameter estimation using full post-Newtonian inspiral waveforms”, Phys. Rev. D, 77, 024030 (2008). [DOI], [ADS], [arXiv:0707.4434 [gr-qc]]. (Cited on page 20.) · doi:10.1103/PhysRevD.77.024030
[411] Tulczyjew, W., “On the energy-momentum tensor density for simple pole particles”, Bull. Acad. Polon. Sci. Cl. III, 5, 279 (1957). (Cited on pages 147, 148, and 150.) · Zbl 0077.42004
[412] Tulczyjew, W., “Motion of multipole particles in general relativity theory”, Acta Phys. Pol., 18, 37 (1959). (Cited on pages 147, 148, and 150.) · Zbl 0087.22802
[413] Vaidya, V., “Gravitational spin Hamiltonians from the <Emphasis Type=”Italic“>S matrix”, Phys. Rev. D, 91, 024017 (2015). [DOI], [arXiv:1410.5348 [hep-th]]. (Cited on page 147.) · doi:10.1103/PhysRevD.91.024017
[414] Vines, J., Hinderer, T. and Flanagan, É.É., “Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals”, Phys. Rev. D, 83, 084051 (2011). [DOI], [arXiv:1101.1673 [gr-qc]]. (Cited on page 16.) · doi:10.1103/PhysRevD.83.084051
[415] Wagoner, R. V., “Test for Existence of Gravitational Radiation”, Astrophys. J. Lett., 196, L63-L65 (1975). [DOI]. (Cited on page 13.) · Zbl 0709.62503 · doi:10.1086/181745
[416] Wagoner, R. V. and Will, C. M., “Post-Newtonian gravitational radiation from orbiting point masses”, Astrophys. J., 210, 764-775 (1976). [DOI]. (Cited on pages 20 and 140.) · doi:10.1086/154886
[417] Wald, R. M., “On perturbations of a Kerr black hole”, J. Math. Phys., 14, 1453-1461 (1973). [DOI]. (Cited on page 110.) · doi:10.1063/1.1666203
[418] Walker, M. and Will, C. M., “The approximation of radiative effects in relativistic gravity: Gravitational radiation reaction and energy loss in nearly Newtonian systems”, Astrophys. J. Lett., 242, L129-L133 (1980). [DOI], [ADS]. (Cited on page 54.) · doi:10.1086/183417
[419] Wen, L., “On the Eccentricity Distribution of Coalescing Black Hole Binaries Driven by the Kozai Mechanism in Globular Clusters”, Astrophys. J., 598, 419 (2003). [DOI], [astro-ph/0211492]. (Cited on page 135.) · doi:10.1086/378794
[420] Wex, N., “The second post-Newtonian motion of compact binary-star systems with spin”, Class. Quantum Grav., 12, 983-1005 (1995). [DOI]. (Cited on pages 138 and 141.) · Zbl 0825.70076 · doi:10.1088/0264-9381/12/4/009
[421] Will, CM; Sasaki, M. (ed.), Gravitational Waves from Inspiralling Compact Binaries: A Post-Newtonian Approach, Proceedings of the 8th Nishinomiya-Yukawa Memorial Symposium, Shukugawa City Hall, Nishinomiya, Hyogo, Japan, 28-29 October, 1993, Tokyo
[422] Will, C. M., “Generation of post-Newtonian gravitational radiation via direct integration of the relaxed Einstein equations”, Prog. Theor. Phys. Suppl., 136, 158-167 (1999). [DOI], [gr-qc/9910057]. (Cited on pages 11, 20, and 50.) · Zbl 1169.83301 · doi:10.1143/PTPS.136.158
[423] Will, C. M., “Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies”, Phys. Rev. D, 71, 084027 (2005). [DOI], [gr-qc/0502039]. (Cited on pages 151 and 159.) · doi:10.1103/PhysRevD.71.084027
[424] Will, C. M. and Wiseman, A. G., “Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order”, Phys. Rev. D, 54, 4813-4848 (1996). [DOI], [gr-qc/9608012]. (Cited on pages 11, 12, 20, 50, 51, and 141.) · doi:10.1103/PhysRevD.54.4813
[425] Wiseman, A. G., “Coalescing binary systems of compact objects to (post)5/2-Newtonian order. II. Higher-order wave forms and radiation recoil”, Phys. Rev. D, 46, 1517-1539 (1992). [DOI], [ADS]. (Cited on page 22.) · doi:10.1103/PhysRevD.46.1517
[426] Wiseman, A. G., “Coalescing binary systems of compact objects to (post)5/2-Newtonian order. IV. The gravitational wave tail”, Phys. Rev. D, 48, 4757-4770 (1993). [DOI], [ADS]. (Cited on page 20.) · doi:10.1103/PhysRevD.48.4757
[427] Wiseman, A. G. and Will, C. M., “Christodoulou’s nonlinear gravitational-wave memory: Evaluation in the quadrupole approximation”, Phys. Rev. D, 44, R2945-R2949 (1991). [DOI]. (Cited on pages 21, 43, and 130.) · doi:10.1103/PhysRevD.44.R2945
[428] Zeng, J. and Will, C. M., “Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling”, Gen. Relativ. Gravit., 39, 1661 (2007). [DOI], [arXiv:0704.2720]. (Cited on page 18.) · Zbl 1181.83034 · doi:10.1007/s10714-007-0475-6
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