Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping

Understand

We study various geometrical aspects of Schroedinger space-times with dynamical exponent z>1 and compare them with the properties of AdS (z=1).

• The Schroedinger metrics are singular for 1<z<2 while the usual Poincare coordinates are incomplete for z \geq 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 Schroedinger space-times admit no global timelike Killing vectors.