How to move a black hole without excision: gauge conditions for the   numerical evolution of a moving puncture
  Recent 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. 
James R. van Meter, John G. Baker, Michael Koppitz, Dae-Il Choi