  The late stage of the inspiral of two black holes may have important
non-Newtonian effects that are unrelated to radiation reaction. To understand
these effects we approximate a slowly inspiralling binary by a stationary
solution to Einstein's equations in which the holes orbit eternally. Radiation
reaction is nullified by specifying a boundary condition at infinity containing
equal amounts of ingoing and outgoing radiation. The computational problem is
then converted from an evolution problem with initial data to a boundary value
problem. In addition to providing an approximate inspiral waveform via
extraction of the outgoing modes, our approximation can give alternative
initial data for numerical relativity evolution. We report results on
simplified models and on progress in building 3D numerical solutions.
