2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/195811Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.8 pages, 13 figures. Edited slightly for clarity as requested by the referee and editor. Also corrected errors due to a misplaced factor of alpha. Main results unchangedGeneral Relativity and Quantum Cosmologytext