4 Non-linear Iteration of the Field Equations
By Theorem 1 we know the most general solution of the linearized equations in the exterior of the
source. We then tackle the problem of the post-Minkowskian iteration of that solution. We consider the full
where the first term is composed of the result given by Eqs. (26, 27, 28). In this article, we shall always
understand the infinite sums such as the one in Eq. (29) in the sense of formal power series, i.e. as an
ordered collection of coefficients, e.g., . We do not attempt to control the mathematical nature of
the series and refer to the mathematical-physics literature for discussion (in the present context, see notably
Refs. [45, 64]).