Geometry of Schrodinger space-times, global coordinates, and harmonic trapping

We study various geometrical aspects of Schrodinger space-times with dynamical exponent z > 1 and compare them with the properties of AdS (z = 1). The Schrodinger metrics are singular for 1 < z < 2 while the usual Poincare coordinates are incomplete for z >= 2. For z = 2 we obtain a global coordinate system and we explain the relations among its geodesic completeness, the choice of global time, and the harmonic trapping of non-relativistic CFTs. For z > 2, we show that the Schrodinger space-times admit no global timelike Killing vectors.