Energy-mom tensor of charged dust (homogeneous and isotropic)

[smallphi]

You have charged dust (pressure = 0, charge density/mass density = given constant). I suppose the total energy-momentum tensor of that system (including the rest energy and the EM field) cannot be expressed simply in terms of the arbitrary 4-velocity of the dust like for example the case of ideal fluid.

That's why, let's specialize to the case of charged dust that is homogeneous and isotropic, basically charged dust that expands in FRW universe. What is the total energy momentum tensor of that system either as an abstract geometric formula involving the 4-velocity of the dust or by components in the comoving coordinates?

I can't find a paper that discusses this case.

 

[Ich]

Sometimes there are stunning coincidences. I started to ponder this question, too, just a few hours ago, because it came up in a discussion.

That's why, let's specialize to the case of charged dust that is homogeneous and isotropic, basically charged dust that expands in FRW universe.

I found only http://adsabs.harvard.edu/abs/1974ApJ...190..279B"old paper. There seem to be some issues with isotropy, basically that a charged universe is impossible in the first place because there are no isotropic vector fields. Sounds logical, but the author claims to overcome this obstacle.
I hope someone can provide answers or links.