General Relativity and Gravitation

, Volume 13, Issue 4, pp 335–359 | Cite as

Equation of motion including the reaction of gravitational radiation

  • A. Papapetrou
  • B. Linet
Research Articles

Abstract

We consider a bounded distribution of perfect fluid in slow motion (Νc), 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.

Keywords

Field Equation Differential Geometry Reaction Force Gravitational Field Radiation Effect 

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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • A. Papapetrou
    • 1
  • B. Linet
    • 1
  1. 1.Equipe de Recherche Associée au CNRS Nℴ533Université Paris VI, Institut Henri PoincaréParis Cedex 05France

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