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 doubt on the soundness of the post-Newtonian series, and (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 paper, we resolve 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 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.
- Received 21 December 2001
DOI:https://doi.org/10.1103/PhysRevD.65.124020
©2002 American Physical Society