Figure 13

Figure 13: This figure shows the expansion Θ for various pretracking surfaces, i.e. for various choices for the shape function H, in a head-on binary black hole collision. Notice how the three shape functions (34View Equation) (here labelled Θ, rΘ, and 2 r Θ) result in pretracking surfaces whose expansions converge smoothly to zero just when the apparent horizon appears (at about t = 1.1). 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.