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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 Tab (i.e. a choice of some physical model describing the source) selects a particular physical exterior solution among our general class.


 5.1 The matching equation
 5.2 General expression of the multipole expansion
 5.3 Equivalence with the Will-Wiseman formalism
 5.4 The source multipole moments
 5.5 Post-Newtonian field in the near zone

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