A correspondence between Maxwell--Einstein theory and superfluidity

TL;DR

This paper unifies electromagnetic and gravitational analogies in superfluid dynamics by formulating a coupled Maxwell and curved space-time theory, revealing a deep correspondence with quantum fluid behavior and vortex metrics.

Contribution

It introduces a novel theoretical framework coupling Maxwell's equations with a conformally curved space-time to unify superfluid electrodynamics and gravity analogies.

Findings

Established a correspondence between Maxwell's equations and superfluid quantum dynamics.

Derived an effective vortex metric with torsional connection components.

Explored the impact of the vortex metric on superfluid electromagnetic equations.

Abstract

A planar superfluid is considered and interpreted in terms of electromagnetism and gravity. It has previously been suggested that the superfluid flow can be regarded as analogous to an electromagnetic field and that a non-vanishing density gradient give rise to a gravity-like force. The present work seeks to reconcile these hitherto distinct pictures into a unified exposition of vortex electrodynamics in a curved analogue space-time. By constructing a theory in which the planar Maxwell's equations are coupled to a (d+1)-dimensional conformally curved space-time, we expose a correspondence between the resulting equations of motion of the embedded fields and the dynamics of a quantum fluid. Finally, an effective vortex metric whose connection components are torsional is studied and its effect on the superfluid Maxwell's equations is elucidated upon.