Eur. Phys. J. Plus (2017) 132: 30
https://doi.org/10.1140/epjp/i2017-11292-4

Regular Article

Covariant theory of Bose-Einstein condensates in curved spacetimes with electromagnetic interactions: The hydrodynamic approach

¹ Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France
² Departamento de Física, Centro de Investigación y Estudios Avanzados del IPN, A.P. 14-740, 07000, México D.F., Mexico

^* e-mail: chavanis@irsamc.ups-tlse.fr

Received: 7 July 2016
Accepted: 10 December 2016
Published online: 23 January 2017

Abstract

We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of weak gravitational fields in a static or expanding background, and the nonrelativistic (Newtonian) limit. The Klein-Gordon-Maxwell-Einstein equations govern the evolution of a complex scalar field, possibly describing self-gravitating Bose-Einstein condensates, coupled to an electromagnetic field. They may find applications in the context of dark matter, boson stars, and neutron stars with a superfluid core.