Simulations of Wald magnetospheres for a^* = 0.5 and M = 1 at t = 128 M_⊙. Left: 3D Cartesian CARPET grid (vacuum spacetime modeled by MACLACHLAN). Right: 2D (axially symmetric) spherical grid (vacuum spacetime modeled by SPHERICALBSSN). The poloidal field is indicated by streamlines, the toroidal field by red and blue colors (color scale coincides for all panels) indicating whether the toroidal field leaves or enters into the displayed plane, respectively. The BH ergosphere is denoted by a solid white line.