Skip to main content
SpringerLink
Log in

Equation of motion including the reaction of gravitational radiation

  • Research Articles
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

We consider a bounded distribution of perfect fluid in slow motion (Ν≪c), the gravitational field being weak everywhere. The equations of motion are derived by a systematic discussion of the field equation:

combined with the conservation law:

The radiative terms of the metric are computed to the order in which radiation effects appear for the first time in the equation of motion. The expression for the gravitational radiation reaction force, appearing as a perturbation of the post-post-Newtonian equation of motion, is determined. This leads to a formula for the rate of energy loss of the system which is equivalent to the formula derived by Chandrasekhar and Esposito. For quasiperiodic motions the formula reduces to the classical Einstein formula for the gravitational quadrupole radiation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Einstein, A., and Grommer, J. (1927).Sitzungsber. Preuss. Akad. Wiss. Berlin Phys.-Math. Kl., 2.

  2. Einstein, A., Infeld, L., and Hoffmann, B. (1938).Ann. Math.,39, 65.

    Google Scholar 

  3. Fock, V. (1939).J. Phys. USSR,1, 81.

    Google Scholar 

  4. Petrova, N. (1949).Zh. Eksp. Teor. Fiz.,19, 989.

    Google Scholar 

  5. Papapetrou, A. (1951).Proc. Phys. Soc. A,64, 57.

    Google Scholar 

  6. Infeld, L. (1938).Phys. Rev.,53, 836.

    Google Scholar 

  7. Hu, N. (1947).Proc. R. Irish Acad.,51A, 87.

    Google Scholar 

  8. Trautman, A. (1958).Bull. Acad. Pol. Sci.,6, 627.

    Google Scholar 

  9. Peres, A. (1960).Nuovo Cimento,15, 351.

    Google Scholar 

  10. Infeld, L. and Michalska-Trautman, R. (1969).Ann. Phys. (N.Y.),55, 561.

    Google Scholar 

  11. Chandrasekhar, S., and Esposito, F. (1970).Astrophys. J.,160, 153.

    Google Scholar 

  12. Ehlers, J., Rosenblum, A., Goldberg, J., and Havas, P. (1976).Astrophys. J.,208, L77.

    Google Scholar 

  13. Anderson, J., and Decanio, T. (1975).Gen. Rel. Grav.,6, 197.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe de Recherche Associée au CNRS Nℴ533, Université Paris VI, Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75231, Paris Cedex 05, France

    A. Papapetrou & B. Linet

Authors
  1. A. Papapetrou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Linet
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Papapetrou, A., Linet, B. Equation of motion including the reaction of gravitational radiation. Gen Relat Gravit 13, 335–359 (1981). https://doi.org/10.1007/BF01025468

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01025468

Keywords

Search

Navigation