Eur. Phys. J. D (2015) 69: 125
https://doi.org/10.1140/epjd/e2015-60062-3

Regular Article

Space-time curvature signatures in Bose-Einstein condensates

¹ Departamento de Física, Centro de Investigación y Estudios Avanzados del IPN A. P. 14–740, 07000 México, D.F., México
² Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290 San Luis Potosí, México

^a Part of the Instituto Avanzado de Cosmología (IAC) collaboration http://www.iac.edu.mx/
^b e-mail: egomez@ifisica.uaslp.mx

Received: 31 January 2015
Received in final form: 13 March 2015
Published online: 8 May 2015

Abstract

We derive a generalized Gross-Pitaevski (GP) equation for a Bose Einstein Condensate (BEC) immersed in a weak gravitational field starting from the covariant Complex Klein-Gordon field in a curved space-time. We compare it with the traditional GP equation where the gravitational field is added by hand as an external potential. We show that there is a small difference of order gz/c² between them that could be measured in the future using Bose-Einstein Condensates. This represents the next order correction to the Newtonian gravity in a curved space-time.