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In recent years post-Newtonian approximations for isolated slowly-movingsystems in general relativity have been studied by means of matched asymptoticexpansions. A paper by Poujade & Blanchet in 2002 made great progress byeffectively reducing the use of such expansions to an algorithmic form. It gavesystematic procedures for the development of both near-zone and far-zoneasymptotic expansions, avoiding the divergent integrals which often bedevilledsuch methods, and showed that these two expansions could be made to matchexactly, a result described there as somewhat remarkable.  This paper revisits that work and shows that there is unfortunately an errorin it which invalidates the results of the matching process as given therein.The present paper identifies that error and shows how it may be corrected togive valid matching results. The correction is presented in a redevelopmentsomewhat different from that of their paper. This shows that far from beingsomewhat remarkable, it is in fact inevitable that the match is exact. It isindeed remarkable that they could carry both expansions to the point at whichmatching becomes possible, but if it can be done at all, then the match isnecessarily exact.  A companion paper will apply this asymptotic matching to a model problem inwhich the correct near-zone expansion was obtained by approximation from anexact solution. It will be shown that there is a discrepancy between thisexpansion and results from the original development of Poujade & Blanchet butthat the corrected development presented here reproduces the result of themodel problem exactly.

Post-Newtonian approximation for isolated systems by matched asymptotic expansions I. General structure revisited