## 5 Exterior Field of a Post-Newtonian Source

By Theorem 2 we control the most general class of solutions of the vacuum equations outside the
source, in the form of non-linear functionals of the source multipole moments. For instance, these
solutions include the Schwarzschild and Kerr solutions, as well as all their perturbations. By
Theorem 4 we learned how to construct the radiative moments at infinity. We now want to
understand how a specific choice of stress-energy tensor (i.e. a choice of some physical
model describing the source) selects a particular physical exterior solution among our general
class.