  We describe a post-Minkowskii approximation of general relativity as a power
series expansion in G, Newton's gravitational constant. Material sources are
hidden behind boundaries, and only the vacuum Einstein equations are
considered. An iterative procedure is described which, in one complete step,
takes any approximate solution of the Einstein equations and produces a new
approximation which has the error decreased by a factor of G. Each step in the
procedure consists of three parts: first the equations of motion are used to
update the trajectories of the boundaries; then the field equations are solved
using a retarded Green's function for Minkowskii space; finally a gauge
transformation is performed which makes the geometry well behaved at future
null infinity. Differences between this approach to the Einstein equations and
similar ones are that we use a general (non-harmonic) gauge and formulate the
procedure in a constructive manner which emphasizes its suitability for
implementation on a computer.

General Relativity and Quantum Cosmology