  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.
