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

• smallphi
In summary, the discussion revolves around the energy-momentum tensor of a system consisting of charged dust with given constant charge density/mass density and pressure. It is mentioned that this tensor cannot be expressed simply in terms of the 4-velocity of the dust, unlike the ideal fluid case. Specializing to the case of homogeneous and isotropic charged dust expanding in a FRW universe, the total energy-momentum tensor is requested in either an abstract geometric formula involving the 4-velocity or by components in comoving coordinates. The conversation also mentions a paper discussing this case, which overcomes the obstacle of isotropy for a charged universe. However, it is mentioned that there are no other known papers on this topic.
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.

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.

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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.

## 1. What is the energy-momentum tensor of charged dust?

The energy-momentum tensor of charged dust is a mathematical quantity used to describe the distribution of energy and momentum of a system of charged particles. It takes into account the density, pressure, and velocity of the particles, and is an important tool in understanding the behavior of charged dust in various physical systems.

## 2. How is the energy-momentum tensor of charged dust calculated?

The energy-momentum tensor of charged dust is calculated using the stress-energy tensor, which is a 4x4 matrix that represents the energy and momentum of a system in spacetime. The specific equation used to calculate the energy-momentum tensor of charged dust takes into account the electric and magnetic fields, as well as the charge density and current density of the particles.

## 3. What properties does the energy-momentum tensor of charged dust have?

The energy-momentum tensor of charged dust has several important properties. First, it is symmetric, meaning that the energy and momentum are conserved in all directions. Additionally, it is traceless, meaning that the total energy and momentum of the system is zero. It is also isotropic, meaning that it does not depend on the direction of observation, and homogeneous, meaning that it is the same at all points in space and time.

## 4. How does the energy-momentum tensor of charged dust relate to Einstein's field equations?

The energy-momentum tensor of charged dust is one of the sources in Einstein's field equations, which describe the relationship between the curvature of spacetime and the distribution of matter and energy within it. It is used to calculate the gravitational effects of charged dust on the curvature of spacetime, and plays a crucial role in understanding the dynamics of charged dust in the universe.

## 5. Can the energy-momentum tensor of charged dust be used in all physical systems?

The energy-momentum tensor of charged dust is a powerful tool that can be used in a wide variety of physical systems, from cosmological models to microscopic particle interactions. However, it is important to note that it is based on certain assumptions, such as the particles being non-interacting and the system being homogeneous and isotropic. In some cases, these assumptions may not hold, and alternative methods may need to be used to accurately describe the energy and momentum of the system.

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