Superfluidity and Stationary Space-Times

TL;DR

This paper explores the analogy between superfluidity and gravitation, showing how vortex models in superfluids relate to stationary space-time metrics and the emergence of G"odel-like universes with closed time-like curves.

Contribution

It establishes a novel connection between superfluid vortex models and stationary gravitational fields, including the derivation of cosmic string and G"odel-like metrics from superfluid dynamics.

Findings

The spinning cosmic string metric models a superfluid vortex gravitational field.

Multiple vortices lead to G"odel-like metrics on large scales.

Closed time-like curves are linked to superfluid rigidity breakdown.

Abstract

A connection between superfluidity and gravitation is established for physical stationary gravitational fields. 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 G\"odel-like metric emerges. In both the single and multiple vortex cases the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity.