  We construct approximate initial data for non-spinning black hole binary
systems by asymptotically matching the 4-metrics of two tidally perturbed
Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian
4-metric in ADMTT coordinates. The specific matching procedure used here
closely follows the calculation in gr-qc/0503011, and is performed in the so
called buffer zone where both the post-Newtonian and the perturbed
Schwarzschild approximations hold. The result is that both metrics agree in the
buffer zone, up to the errors in the approximations. However, since isotropic
coordinates are very similar to ADMTT coordinates, matching yields better
results than in the previous calculation, where harmonic coordinates were used
for the post-Newtonian 4-metric. In particular, not only does matching improve
in the buffer zone, but due to the similarity between ADMTT and isotropic
coordinates the two metrics are also close to each other near the black hole
horizons. With the help of a transition function we also obtain a global smooth
4-metric which has errors on the order of the error introduced by the more
accurate of the two approximations we match. This global smoothed out 4-metric
is obtained in ADMTT coordinates which are not horizon penetrating. In
addition, we construct a further coordinate transformation that takes the
4-metric from global ADMTT coordinates to new coordinates which are similar to
Kerr-Schild coordinates near each black hole, but which remain ADMTT further
away from the black holes. These new coordinates are horizon penetrating and
lead, for example, to a lapse which is everywhere positive on the t=0 slice.
Such coordinates may be more useful in numerical simulations.
