Space-Time Curvature Signatures in Bose-Einstein Condensates

TL;DR

This paper derives a generalized Gross-Pitaevskii equation incorporating gravitational effects from curved spacetime, predicting measurable differences in Bose-Einstein Condensates that extend Newtonian gravity corrections.

Contribution

It introduces a covariant derivation of the GP equation in curved spacetime, highlighting a small measurable correction due to gravity in BEC experiments.

Findings

Derived a covariant GP equation in curved spacetime.

Identified a measurable gravitational correction of order g z/c^2.

Proposed potential experimental detection of relativistic gravity effects in BECs.

Abstract

We derive a generalized Gross-Pitaevski (GP) equation immersed on a electromagnetic and a weak gravitational field starting from the covariant Complex Klein-Gordon field in a curved space-time. We compare it with the GP equation where the gravitational field is added by hand as an external potential. We show that there is a small difference of order $g z/c^2$ between them that could be measured in the future using Bose-Einstein Condensates (BEC). This represents the next order correction to the Newtonian gravity in a curved space-time.