The harmonic conditions consist of wave equations which can be used to propagate the gauge as four
scalar waves using characteristic evolution. This allows the extraction world tube to be placed at a finite
distance from the injection world tube 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 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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