## 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
post-Minkowskian series
where the first term is composed of the result given by Equations (26, 27, 28). In this article, we shall
always understand the infinite sums such as the one in Equation (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 Refs. [72, 100, 187, 188, 189]).