The Godel-Schrodinger Spacetime and Stringy Chronology Protection

Abstract

We show that the null Melvin map applied to a rotational isometry of global anti-de Sitter space produces a spacetime with properties analogous to both the Godel and Schrodinger geometries. The isometry group of this Godel-Schrodinger spacetime is appropriate to provide a holographic dual for the same non-relativistic conformal theory as the ordinary Schrodinger geometry, but defined on a sphere. This spacetime also possesses closed timelike curves outside a certain critical radius. We show that a holographic preferred screen for an observer at the origin sits at an interior radius, suggesting that a holographic dual description would only require the chronologically consistent region. Additionally, giant graviton probe branes experience repulson-type instabilities in the acausal region, suggesting a condensation of branes will modify the pathological part of the geometry to remove the closed timelike curves.

28 pages, 2 figures, LaTeX. v2: references added. v3: version to appear in JHEP

References in corpus (13)

• Gravity duals for non-relativistic CFTs
• Holography for Schrodinger backgrounds
• Families of IIB duals for nonrelativistic CFTs
• Solutions of type IIB and D=11 supergravity with Schrodinger(z) symmetry
• Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
• The particle number in Galilean holography
• Supersymmetric non-relativistic geometries in M-theory
• Non-relativistic metrics with extremal limits
• Universality and exactness of Schrodinger geometries in string and M-theory
• Properties of Schroedinger Black Holes from AdS Space
• Geometry and Phase Structure of Non-Relativistic Branes
• Towards a Non-Relativistic Holographic Superfluid
• Chronology protection and the stringy exclusion principle

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• Hyperscaling violation : a unified frame for effective holographic theories
• Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime