Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
High Energy Physics - Theory
2009-07-22 v2 General Relativity and Quantum Cosmology
Abstract
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.
Keywords
Cite
@article{arxiv.0904.3304,
title = {Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping},
author = {Matthias Blau and Jelle Hartong and Blaise Rollier},
journal= {arXiv preprint arXiv:0904.3304},
year = {2009}
}
Comments
15 pages, v2: some comments and references added