General Relativity and Gravitation

, Volume 18, Issue 3, pp 255–270 | Cite as

The ADM Hamiltonian at the postlinear approximation

  • Gerhard Schäfer
Research Articles


The ADM Hamiltonian for a many-particle system is calculated up to the postlinear approximation, i.e., to the approximation that both the equations of motion for the particles and the equations of motion for the gravitational field in case of no-incoming radiation correctly result up to the postlinear approximation. The relation of this Hamiltonian to the ADM Hamiltonian obtained by a post-Newtonian approximation scheme which was applied up to the first radiation-reaction and radiation levels is discussed. From here the standard formulas for the mechanical angular momentum and energy losses as well as the radiated energy and angular momentum are deduced. Background logarithmic and logarithmic radiative terms are shown to be not present at our approximation if the condition of no-incoming radiation is fulfilled.


Radiation Angular Momentum Energy Loss Differential Geometry Gravitational Field 
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  1. 1.
    Westpfahl, K., and Goller, M. (1979).Lett. Nuovo Cimento,26, 573; Westpfahl, K., and Hoyler, H. (1980).Lett. Nuovo Cimento,27, 581.Google Scholar
  2. 2.
    Bel, L., Damour, T., Deruelle, N., Ibañez, J., and Martin, J. (1981).Gen. Rel. Grav.,13, 963.Google Scholar
  3. 3.
    Damour, T., and Deruelle, N. (1981).Phys. Lett.,87A, 81.Google Scholar
  4. 4.
    Deruelle, N. (1983). InProceedings of the Third Marcel Grossmann Meeting on General Relativity, N. Hu, ed. (North-Holland, Amsterdam), p. 955.Google Scholar
  5. 5.
    Damour, T. (1982).C. R. Acad. Sci. Paris,294, Série II, 1355.Google Scholar
  6. 6.
    Damour, T. (1983). InProceedings of the Third Marcel Grossmann Meeting on General Relativity, N. Hu, ed. (North-Holland, Amsterdam), p. 583.Google Scholar
  7. 7.
    Damour, T. (1983). InGravitational Radiation, N. Deruelle and T. Piran, eds. (North-Holland, Amsterdam).Google Scholar
  8. 8.
    Arnowitt, R., Deser, S., and Misner, C. W. (1962). InGramtation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York).Google Scholar
  9. 9.
    Ohta, T., Okamura, H., Kimura, T., and Hiida, K. (1974).Prog. Theor. Phys.,51, 1598.Google Scholar
  10. 10.
    Schäfer, G. (1985).Ann. Phys. (N.Y.),161, 81.Google Scholar
  11. 11.
    Damour, T., and Schäfer, G. (1985).Gen. Rel. Grav.,17, 879.Google Scholar
  12. 12.
    DeWitt, B. S. (1967).Phys. Rev.,160, 1113.Google Scholar
  13. 13.
    Regge, T., and Teitelboim, C. (1974).Ann. Phys. (N.Y.),88, 286.Google Scholar
  14. 14.
    Rosenblum, A. (1978).Phys. Rev. Lett.,41, 1003; (1981).Phys. Lett.,81A, 1.Google Scholar
  15. 15.
    Fock, V. (1960).Theorie von Raum, Zeit und Gravitation (Akademie-Verlag, Berlin), Section 87.Google Scholar
  16. 16.
    Isaacson, R. A., and Winicour, J. (1968).Phys. Rev.,168, 1451.Google Scholar
  17. 17.
    Madore, J. (1970).Ann. Inst. Henri Poincaré,12, 365.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Gerhard Schäfer
    • 1
  1. 1.Fakultät für Physik der Universität KonstanzKonstanzFederal Republic of Germany

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