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Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions | | Olivier Poujade
; Luc Blanchet
; | | Date: |
21 Dec 2001 | | Journal: | Phys.Rev. D65 (2002) 124020 | | Subject: | gr-qc | | Abstract: | 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. | | Source: | arXiv, gr-qc/0112057 | | Services: | Forum | Review | PDF | Favorites | |
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