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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
+ sum oo hab = Gnhab , (29) ext n=1 n
where the first term is composed of the result given by Equations (26View Equation, 27View Equation, 28View Equation). In this article, we shall always understand the infinite sums such as the one in Equation (29View Equation) in the sense of formal power series, i.e. as an ordered collection of coefficients, e.g., ( ) hab n n (- N. 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. [72100187Jump To The Next Citation Point188Jump To The Next Citation Point189Jump To The Next Citation Point]).


 4.1 The post-Minkowskian solution
 4.2 Generality of the solution
 4.3 Near-zone and far-zone structures
 4.4 The radiative multipole moments

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