  The periodic standing wave method studies circular orbits of compact objects
coupled to helically symmetric standing wave gravitational fields. From this
solution an approximation is extracted for the strong field, slowly
inspiralling motion of binary black holes and binary neutron stars. Previous
work on this project has developed a method using a few multipoles of specially
adapted coordinates well suited both to the radiation and the source regions.
This method had previously been applied to linear and nonlinear scalar field
models, to linearized gravity, and to a post-Minkowski approximation. Here we
present the culmination of this approach: the application of the method in full
general relativity. The fundamental equations had previously been developed and
the challenge presented by this step is primarily a computational one which was
approached with an innovative technique. The numerical results of these
computations are compared with the corresponding results from linearized and
post-Minkowksi computations.
