The Green's function method, classical for a linear wave equation, is generalized to a nonlinear field theory and, specifically, to general relativity. The general structure of a Lorentz-invariant perturbation expansion in terms of the gravitational constant is studied. It is found that the nth order contribution can be expressed with the help of a set of generalized Green's functions, depending on n events on the “sources” and the event at which the field is wanted. The ‘sources” include not only the ordinary matter, but also the initial conditions which are prescribed to the metric field to determine it uniquely. The generalized Green's functions are studied with the help of a graphical representation which makes clear how the nonlinearity of the equations affects the propagation of grativational action. Its “scattering” by the sources and by the field itself produces the result that every event inside the light cone may contribute to the force on a particle at its vertex; the equations of motion have therefore an integro-differential structure. The general formalism is applied to the second approximation; the equations of motion, with an accuracy up to the second order, and the relevant generalized Green's function are computed.
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