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

2009/04/30 by Matthias Blau, Jelle Hartong, Blaise Rollier · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #gr-qc #hep-th

paper · pdf · doi:10.1088/1126-6708/2009/07/027

published as JHEP 0907:027,2009 · 15 pages, v2: some comments and references added

arxiv created 2009/04/30 · openalex publication_date 2009/07/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 ≥ 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.

Cited by

• Non-relativistic metrics with extremal limits
• Schrödinger invariant solutions of M-theory with enhanced supersymmetry
• Black probes of Schrödinger spacetimes
• From D3-branes to Lifshitz spacetimes

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