11.2 Adaptive mesh refinement for BBH in higher dimensional gravity

In [439] 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 11View Image 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 Gim, where the indices i and m denote the refinement level and component number, respectively. At the spherical boundary, marked by X, 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].
View Image

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 [438]; copyright by APS.

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