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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