Figure 13: This figure shows the expansion for various pretracking surfaces, i.e. for various
choices for the shape function , in a head-on binary black hole collision. Notice how the three
shape functions (34) (here labelled , , and ) result in pretracking surfaces whose
expansions converge smoothly to zero just when the apparent horizon appears (at about ).
Notice also that these three expansions have all converged to each other somewhat before the common
apparent horizon appears. Figure reprinted with permission from [135]. © 2005 by the American
Physical Society.
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