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I see that we use perfect fluid which is characterized by a energy density and isotropic pressure for general forms of matter.

When guessing the values of energy momentum tensor indices we can use the physical insight that they are the flux of four momentum in a constant surface of spacetime.

The shortcut to find the general tensorial equation is making physical arguments in the "rest" frame.

Clearly the sheer stresses vanish and therefore only pressure remains in three orthogonal directions and the Energy Momentum matrix is diagonal.

What is not clear to me is how a rest frame makes sense in the case of a perfect fluid. Are we assuming an infinitesimal element of the fluid? Otherwise for the bulk of the fluid a rest frame is not possible given the random motions of particles.

Also related is that what does mean pressure for the elements of fluid when that element is on the boundary as opposed to be inside the fluid.

Put it other way, what does pressure, the spatial diagonal elements in the EM tensor, in the rest frame, means on "the surface of a perfect fluid", say a star?

Does it mean that in a thought experiment if we put a rod close enough to the surface of a star we will sense a pushing force against us?

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What is not clear to me is how a rest frame makes sense in the case of a perfect fluid. Are we assuming an infinitesimal element of the fluid? Otherwise for the bulk of the fluid a rest frame is not possible given the random motions of particles.

Perfect fluid is usually assumed to undergo motion that can be described by continuous velocity field. Due to this continuity, it is possible to pick up any point and its neighborhood in which other particles have very similar velocities. The velocity of the point then defines the reference frame in which the point is at rest and its neighborhood moves slowly.

Also related is that what does mean pressure for the elements of fluid when that element is on the boundary as opposed to be inside the fluid. Put it other way, what does pressure, the spatial diagonal elements in the EM tensor in the rest frame means on the surface of a perfect fluid, say a star? Does it mean that in a thought experiment if we put a rod close enough to the surface of a star we will sense a pushing force against us?

If pressure is the genuine pressure due to contact with matter, there will be force on the rod. If you mean the magnetic components of the EM stress tensor, then these do have dimension of pressure but do not actually mean there is a pressure-like force acting on the rod surface in the vacuum. The rod may feel force due to EM field but this EM force cannot generally be expressed as surface integral of stress tensor.

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