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

TL;DR

This paper presents a covariant hydrodynamic framework for Bose-Einstein condensates in curved spacetimes, integrating quantum mechanics, electromagnetism, and gravity, with potential applications in astrophysics and dark matter research.

Contribution

It introduces a comprehensive hydrodynamic formulation of Klein-Gordon-Maxwell-Einstein equations applicable to various gravitational regimes.

Findings

Derived hydrodynamic equations for Bose-Einstein condensates in curved spacetime.

Analyzed nonrelativistic and weak-field limits.

Potential applications in dark matter and astrophysical objects.

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.