ar X iv : g r - qc / 0 40 70 33 v 2 5 M ay 2 00 5 Superfluid Picture for Rotating Space - Times

A new prescription, in the framework of condensate models for space-times, for physical stationary gravitational fields is presented. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager-Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a Gödel-like metric emerges. In both the single and multiple vortex cases the failure of general relativity exemplified by the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity.