In the 3+1 formalism, the choice of the coordinate system is given in terms of the gauge variables: the lapse function α and the shift vector βi. However, Einstein's equations say nothing about how the gauge variables should be chosen. This chapter describes the most common gauge conditions used in practice in numerical relativity. Topics covered include slicing conditions, geodesic slicing and focusing, maximal slicing, maximal slices of Schwarzschild, hyperbolic slicing conditions, singularity avoidance for hyperbolic slicing, shift conditions, elliptic shift conditions, evolution type shift conditions, and corotating coordinates.
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