Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions

Details Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions

2001-12-21

arxiv.org/abs/gr-qc/0112057v2

Phys.Rev. D65 (2002) 124020

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

61 pages, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.65.124020

Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness of the post-Newtonian series; (ii) the domain of validity of the approximation which is limited to the near-zone of the source, and prevents one, a priori, from incorporating the condition of no-incoming radiation, to be imposed at past null infinity. In this article, we resolve the problem (i) by iterating the post-Newtonian hierarchy of equations by means of a new (Poisson-type) integral operator that is free of divergencies, and the problem (ii) by matching the post-Newtonian near-zone field to the exterior field of the source, known from previous work as a multipolar-post-Minkowskian expansion satisfying the relevant boundary conditions at infinity. As a result, we obtain an algorithm for iterating the post-Newtonian series up to any order, and we determine the terms, present in the post-Newtonian field, that are associated with the gravitational-radiation reaction onto an isolated slowly-moving matter system.

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