Theoretical and Mathematical Physics

, Volume 142, Issue 1, pp 138–152 | Cite as

Obtaining equations of motion for charged particles in the (v/c)3-approximation by the Einstein-Infeld-Hoffmann method

  • M. V. Gorbatenko
Article

Abstract

We consider some principal methodological problems that appear when the Einstein-Infeld-Hoffmann method is used to find approximate solutions of the general relativity equations and to obtain information about the motion of particles whose interaction force is much greater than the gravitational attraction force. Among these problems are normalizing approximate expressions by expanding exact solutions written in the same coordinate conditions used in the Einstein-Infeld-Hoffmann method, assigning the smallness orders depending on relations between the smallness parameters in play, and verifying cancellations of divergent terms arising in surface integrals. Solving these questions in accordance with the internal logic of the Einstein-Infeld-Hoffmann method results in new tools and techniques for applying the method. We demonstrate these tools and techniques in the example of the problem of the motion of two electrically charged pointlike particles in the (v/c)3-approximation.

Keywords

Einstein-Infeld-Hoffmann method equations of motion in post-post-Coulomb approximation radiation friction force 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. V. Gorbatenko
    • 1
  1. 1.Russian Federal Nuclear CenterAll-Russian Research Institute for Experimental PhysicsSarov, Nizhny Novgorod OblastRussia

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