  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.
