The harmonic conditions consist of wave equations for the coordinates which can be used to
propagate the gauge as four scalar waves using characteristic evolution. This allows the extraction
worldtube to be placed at a finite distance from the injection worldtube without introducing a
gauge ambiguity. Furthermore, the harmonic gauge conditions are the only constraints on the
Cauchy formalism so that gauge propagation also insures constraint propagation. This allows
the Cauchy data to be supplied in numerically benign Sommerfeld form, without introducing
constraint violation. Using random initial data, robust stability of the CCM algorithm was
confirmed for 2000 crossing times on a 453 Cauchy grid. Figure 7 shows a sequence of profiles of
the metric component
as a linearized wave propagates cleanly through the
spherical injection boundary and passes to the characteristic grid, where it is propagated to
.
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