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.

 

[Entropia]

The total energy-momentum tensor of a system can be expressed in terms of the matter content, the electromagnetic field, and the gravitational field. In the case of charged dust, the matter content is described by the charge density and mass density, while the electromagnetic field is determined by the charge density and the motion of the charged particles. However, in general, the total energy-momentum tensor cannot be expressed simply in terms of the arbitrary 4-velocity of the dust, as the motion of the particles is affected by both the gravitational and electromagnetic fields.

In the case of a homogeneous and isotropic charged dust expanding in a FRW universe, the total energy-momentum tensor can be expressed as an abstract geometric formula involving the 4-velocity of the dust. This formula takes into account the expansion of the universe and the effects of both the gravitational and electromagnetic fields on the motion of the charged particles. However, there may not be a specific paper that discusses this exact scenario, as it is a highly specialized case and may not have been extensively studied.

Alternatively, the total energy-momentum tensor can also be expressed in terms of its components in the comoving coordinates, which can be calculated using the Einstein field equations and the equations of motion for the charged dust. This approach may be more straightforward, but it also requires a deeper understanding of general relativity and electromagnetism.

Overall, the total energy-momentum tensor of a charged dust system is a complex and highly dependent on the specific conditions and parameters of the system. It cannot be simplified to a single formula or expression, but rather must be calculated using the appropriate equations and considerations for the given scenario.