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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

Clifford M. Will*

  • Groupe Gravitation Relativiste et Cosmologie (GReCO) Institut d’Astrophysique, 98 bis Boulevard Arago, 75014 Paris, France
  • McDonnell Center for the Space Sciences, Department of Physics, Washington University, St. Louis, Missouri 63130, USA†

  • *Email address: cmw@wuphys.wustl.edu Electronic address: wugrav.wustl.edu/people/CMW
  • †Permanent address.
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Phys. Rev. D 71, 084027 – Published 26 April, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.084027

Abstract

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)5] and O[(v/c)7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5 PN order, we determine the spin-orbit induced reaction effects on the orbital motion, but we find that radiation damping has no effect on either the magnitude or the direction of the spins. Using the equations of motion, we find that the loss of total energy and total angular momentum induced by spin-orbit effects precisely balances the radiative flux of those quantities calculated by Kidder et al. The equations of motion may be useful for evolving inspiraling orbits of compact spinning binaries.

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References (27)

  1. M. E. Pati and C. M. Will, Phys. Rev. D 62, 124015 (2000).
  2. M. E. Pati and C. M. Will, Phys. Rev. D 65, 104008 (2002).
  3. T. Damour and N. Deruelle, Phys. Lett. A87, 81 (1981).
  4. T. Damour, in S. W. Hawking and W. Israel300 Years of Gravitation, edited by (Cambridge University Press, London, 1987), p. 128.
  5. S. M. Kopeikin, Sov. Astron. 29, 516 (1985).
  6. L. P. Grishchuk and S. M. Kopeikin, in Relativity in Celestial Mechanics and Astrometry, edited by J. Kovalevsky and V. A. Brumberg (Reidel, Dordrecht, 1986), p. 19.
  7. L. Blanchet, G. Faye, and B. Ponsot, Phys. Rev. D 58, 124002 (1998).
  8. Y. Itoh, T. Futamase, and H. Asada, Phys. Rev. D 63, 064038 (2001).
  9. B. R. Iyer and C. M. Will, Phys. Rev. Lett. 70, 113 (1993).
  10. B. R. Iyer and C. M. Will, Phys. Rev. D 52, 6882 (1995).
  11. S. Nissanke and L. Blanchet, Classical Quantum Gravity (to be published).
  12. L. E. Kidder, C. M. Will, and A. G. Wiseman, Phys. Rev. D 47, R4183 (1993).
  13. L. E. Kidder, Phys. Rev. D 52, 821 (1995).
  14. E. Poisson and C. M. Will, Phys. Rev. D 52, 848 (1995).
  15. C. Cutler, Phys. Rev. D 57, 7089 (1998).
  16. S. A. Hughes, Mon. Not. R. Astron. Soc. 331, 805 (2002).
  17. A. Vecchio, Phys. Rev. D 70, 042001 (2004).
  18. E. Berti, A. Buonanno, and C. M. Will, Phys. Rev. D 71, 084025 (2005).

  19. In discussions of inspiralling compact binaries, one often sees the statement that spin-orbit terms are 1.5 PN order. This is because, for such system, one treats the radius as being of order m, and the rotational velocity V as being of order unity (especially for rapidly rotating black holes); consequently, the spin-orbit term in this case is effectively of order (m2/r)(m/r)v∼ϵ3/2EN. Because the equations derived in this paper apply to arbitrary systems treatable with PN methods, we will stick with the formal PN ordering of spin terms.

  20. A. Papapetrou, Proc. R. Soc. London Sect. A 209, 248 (1951).
  21. E. Corinaldesi and A. Papapetrou, Proc. R. Soc. London Sect. A 209, 259 (1951).
  22. G. O’brien, Gen. Relativ. Gravit. 10, 129 (1979).
  23. B. M. Barker and R. F. O’Connell, Phys. Rev. D 2, 1428 (1970).
  24. B. M. Barker and R. F. O’Connell, Phys. Rev. D 12, 329 (1975).
  25. B. M. Barker and R. F. O’Connell, Gen. Relativ. Gravit. 11, 149 (1979).
  26. See, for example, Sec. 36.8 of C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
  27. B. M. Barker and R. F. O’Connell, Gen. Relativ. Gravit. 5, 539 (1974).

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Phys. Rev. D 71, 084027– Published 26 April, 2005
  • Received 10 February 2005

© 2005 American Physical Society

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