11.2 Adaptive mesh refinement for BBH in higher dimensional gravity
In  the authors numerically evolved black-hole binaries “in a box” by imposing reflecting
outer boundary conditions, which mimic the anti-de Sitter spacetime. These conditions are
imposed on all the fields and the outer boundary is taken to have spherical shape, which is
approximated by a “Lego” sphere. Figure 11 on the left illustrates a Lego-sphere around a
black-hole binary, mimicking an asymptotically anti-de Sitter spacetime. A computational domain is
schematically displayed using four refinement levels with one or two components each. The
individual components are labeled , where the indices and denote the refinement level
and component number, respectively. At the spherical boundary, marked by , reflecting
boundary conditions were imposed. The right figure shows mesh refinement around two black
holes, with the apparent horizons represented by the white grid. Further extensions of this
research program to numerically study black holes in higher-dimensional gravity can be found
in [441, 437].
Figure 11: Left: Lego-sphere around a black-hole binary. Right: Mesh refinement around two
black holes. Courtesy: Vitor Cardoso, Ulrich Sperhake and Helvi Witek. Reprinted with permission
from ; copyright by APS.