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Abstract

The puncture method for black holes in numerical relativity has recently been extended to punctures that move across the grid, which has led to significant advances in numerical simulations of black-hole binaries. We examine how and why the method works. The coordinate singularity and hence the geometry at the puncture are found to change during evolution, but sufficient regularity is maintained for the numerics to work. We construct an analytic solution for the stationary state of a black hole in spherical symmetry that matches the numerical result and demonstrates that the numerics are not dominated by artefacts at the puncture but indeed find the analytical result.