Comptes Rendus
General relativistic dynamics of compact binary systems
[Dynamique des systèmes binaires compacts en relativité générale]
Comptes Rendus. Physique, Volume 8 (2007) no. 1, pp. 57-68.

Les équations du mouvement d'un système binaire d'objets compacts ont étées calculées dans l'approximation post-newtonienne (PN) de la relativité générale. Le niveau d'approximation atteint l'ordre 3.5PN. La partie conservative des équations du mouvement (obtenue en négligeant les termes de freinage de rayonnement) se déduit d'un lagrangien généralisé en coordonnées harmoniques, et, de façon équivalente, d'un hamiltonien ordinaire en coordonnées ADM. Comme application nous étudions le problème de la stabilité dynamique, vis-à-vis des perturbations gravitationnelles, des orbites binaires circulaires à l'ordre 3PN. Nous trouvons qu'il n'y a pas de dernière orbite stable circulaire ou ISCO à l'ordre 3PN pour des masses égales.

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application, we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses.

Publié le :
DOI : 10.1016/j.crhy.2006.11.004
Keywords: Post-Newtonian theory, Equations of motion, Compact binary systems
Mot clés : Théorie post-newtonienne, Équations du mouvement, Systèmes binaires compacts
@article{CRPHYS_2007__8_1_57_0,
     author = {Luc Blanchet},
     title = {General relativistic dynamics of compact binary systems},
     journal = {Comptes Rendus. Physique},
     pages = {57--68},
     publisher = {Elsevier},
     volume = {8},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crhy.2006.11.004},
     language = {en},
}
TY  - JOUR
AU  - Luc Blanchet
TI  - General relativistic dynamics of compact binary systems
JO  - Comptes Rendus. Physique
PY  - 2007
SP  - 57
EP  - 68
VL  - 8
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crhy.2006.11.004
LA  - en
ID  - CRPHYS_2007__8_1_57_0
ER  - 
%0 Journal Article
%A Luc Blanchet
%T General relativistic dynamics of compact binary systems
%J Comptes Rendus. Physique
%D 2007
%P 57-68
%V 8
%N 1
%I Elsevier
%R 10.1016/j.crhy.2006.11.004
%G en
%F CRPHYS_2007__8_1_57_0
Luc Blanchet. General relativistic dynamics of compact binary systems. Comptes Rendus. Physique, Volume 8 (2007) no. 1, pp. 57-68. doi : 10.1016/j.crhy.2006.11.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.11.004/

[1] H.A. Lorentz; J. Droste Versl. K. Akad. Wet. Amsterdam, Collected Papers of H.A. Lorentz, 26 (1917), p. 392 (and 649, vol. 5, 1937)

[2] A.S. Eddington; G.L. Clark Proc. Phys. Soc. London A, 166 (1938), p. 465

[3] A. Einstein; L. Infeld; B. Hoffmann The gravitational equations and the problem of motion, Ann. Math., Volume 39 (1938), pp. 65-100

[4] V.A. Fock Theory of Space, Time and Gravitation, Pergamon, London, 1959

[5] A. Papapetrou Equations of motion in general relativity, Proc. Phys. Soc. London B, Volume 64 (1951), pp. 57-75

[6] T. Ohta; H. Okamura; T. Kimura; K. Hiida Physically acceptable solution of Einstein's equation for many-body system, Prog. Theor. Phys., Volume 50 (1973), pp. 492-514

[7] T. Ohta; H. Okamura; T. Kimura; K. Hiida Higher-order gravitational potential for many-body system, Prog. Theor. Phys., Volume 51 (1974), pp. 1220-1238

[8] T. Ohta; H. Okamura; T. Kimura; K. Hiida Coordinate condition and higher-order gravitational potential in canonical formalism, Prog. Theor. Phys., Volume 51 (1974), pp. 1598-1612

[9] J.H. Taylor; L.A. Fowler; P.M. McCulloch Measurements of general relativistic effects in the binary pulsar psr1913+16, Nature, Volume 277 (1979), pp. 437-440

[10] J.H. Taylor Pulsar timing and relativistic gravity, Class. Quant. Grav., Volume 10 (1993), pp. 167-174

[11] L. Bel; T. Damour; N. Deruelle; J. Ibanez; J. Martin Poincaré invariant gravitational field and equations of motion of two point-like objects: The postlinear approximation of general relativity, Gen. Relativ. Gravit., Volume 13 (1981), p. 963

[12] T. Damour; N. Deruelle Radiation reaction and angular momentum loss in small angle gravitational scattering, Phys. Lett. A, Volume 87 (1981), p. 81

[13] T. Damour; N. Deruelle Lagrangien généralisé du système de deux masses ponctuelles, à l'approximation post-post-newtonienne de la relativité générale, C. R. Acad. Sci. Paris, Volume 293 (1981), p. 537

[14] T. Damour Gravitational radiation and the motion of compact bodies (N. Deruelle; T. Piran, eds.), Gravitational Radiation, North-Holland Company, Amsterdam, 1983, pp. 59-144

[15] T. Damour; G. Schäfer Gen. Relativ. Gravit., 17 (1985), p. 879

[16] L.P. Grishchuk; S.M. Kopeikin Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force (J. Kovalevsky; V.A. Brumberg, eds.), Relativity in Celestial Mechanics and Astrometry, Reidel, Dordrecht, 1986, pp. 19-33

[17] L. Blanchet; G. Faye; B. Ponsot Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order, Phys. Rev. D, Volume 58 (1998) (124002)

[18] Y. Itoh; T. Futamase; H. Asada Equation of motion for relativistic compact binaries with the strong field point particle limit: The second and half post-Newtonian order, Phys. Rev. D, Volume 63 (2001) (064038)

[19] P. Jaranowski; G. Schäfer Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems, Phys. Rev. D, Volume 57 (1998), pp. 7274-7291

[20] P. Jaranowski; G. Schäfer Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part, Phys. Rev. D, Volume 60 (1999) (124003-1–12403-7)

[21] T. Damour; P. Jaranowski; G. Schäfer Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem, Phys. Rev. D, Volume 62 (2000) 021501(R) Phys. Rev. D, 63, 2000 029903(E), Erratum

[22] T. Damour; P. Jaranowski; G. Schäfer Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries, Phys. Rev. D, Volume 63 (2001) 044021 Phys. Rev. D, 66, 2002 029901(E), Erratum

[23] L. Blanchet; G. Faye Equations of motion of point-particle binaries at the third post-Newtonian order, Phys. Lett. A, Volume 271 (2000), p. 58

[24] L. Blanchet; G. Faye General relativistic dynamics of compact binaries at the third post-Newtonian order, Phys. Rev. D, Volume 63 (2001), p. 062005

[25] L. Blanchet; G. Faye Hadamard regularization, J. Math. Phys., Volume 41 (2000), pp. 7675-7714

[26] L. Blanchet; G. Faye Lorentzian regularization and the problem of point-like particles in general relativity, J. Math. Phys., Volume 42 (2001), pp. 4391-4418

[27] V.C. de Andrade; L. Blanchet; G. Faye Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms, Class. Quant. Grav., Volume 18 (2001), pp. 753-778

[28] L. Blanchet; B.R. Iyer Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame, Class. Quant. Grav., Volume 20 (2003), p. 755

[29] T. Damour; P. Jaranowski; G. Schäfer Dimensional regularization of the gravitational interaction of point masses, Phys. Lett. B, Volume 513 (2001), pp. 147-155

[30] L. Blanchet; T. Damour; G. Esposito-Farèse Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates, Phys. Rev. D, Volume 69 (2004) (124007)

[31] Y. Itoh; T. Futamase Phys. Rev. D, 68 (2003) 121501(R)

[32] Y. Itoh Phys. Rev. D, 69 (2004) (064018)

[33] B.R. Iyer; C.M. Will Post-Newtonian gravitational-radiation reaction for two-body systems, Phys. Rev. Lett., Volume 70 (1993), pp. 113-116

[34] B.R. Iyer; C.M. Will Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies, Phys. Rev. D, Volume 52 (1995), pp. 6882-6893

[35] P. Jaranowski; G. Schäfer Radiative 3.5 post-Newtonian ADM Hamiltonian for many body point-mass systems, Phys. Rev. D, Volume 55 (1997), pp. 4712-4722

[36] M.E. Pati; C.M. Will 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, Volume 65 (2002) (104008)

[37] C. Königsdörffer; G. Faye; G. Schäfer Phys. Rev. D, 68 (2003) (044004)

[38] S. Nissanke; L. Blanchet Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order, Class. Quant. Grav., Volume 22 (2005), p. 1007

[39] T. Mora; C.M. Will A post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects, Phys. Rev. D, Volume 69 (2004) (104021)

[40] L.E. Kidder; C.M. Will; A.G. Wiseman Spin effects in the inspiral of coalescing compact binaries, Phys. Rev. D, Volume 47 (1993), p. R4183-R4187

[41] L. Blanchet Innermost circular orbit of binary black holes at the third post-Newtonian approximation, Phys. Rev. D, Volume 65 (2002) (124009)

[42] T. Damour; B.R. Iyer; B.S. Sathyaprakash Improved filters for gravitational waves from inspiraling compact binaries, Phys. Rev. D, Volume 57 (1998), pp. 885-907

[43] A. Buonanno; T. Damour Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D, Volume 59 (1999) (084006)

Cité par Sources :

Commentaires - Politique