The Godel-Schrodinger Spacetime and Stringy Chronology Protection
  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. 
Charles Max Brown and Oliver DeWolfe
hep-th