Choice of foliation and spatial coordinates

Abstract

We discuss here the choice of spacetime coordinates, from a 3 + 1 point of view. This amounts to discuss first the choice of foliation, via the lapse function: the geodesic, maximal, harmonic, and 1+log slicings are presented here. In a second stage, we focus on of the propagation of the spatial coordinates from slice to slice, via the choice of the shift vector. We introduce the concepts of normal coordinates, minimal distortion and variants of it, Gamma freezing coordinates and Gamma drivers. Finally we discuss choices that fix fully the spatial coordinates on a given slice: spatial harmonic coordinates and Dirac gauge. © 2012 Springer-Verlag Berlin Heidelberg.