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If I understand correctly, an ideal gas has viscosity (i.e. shear stress) whereas a perfect fluid does not. So I am right in thinking that the stress-energy tensor for an ideal gas should not be diagonal, but rather should incorporate shear stress terms?

If not, why not, and if so, how are these terms calculated from the density, pressure, and temperature of the ideal gas? I can't find the stress-energy tensor for an ideal gas anywhere online; I only see results for a perfect fluid.

I don't quite understand this sentence from Wikipedia:

"In other words, the stress energy tensor in engineering differs from the relativistic stress–energy tensor by a momentum-convective term".

"Momentum-convection" seems like a perfect name for the process that causes an ideal gas to be viscous, but I don't know if that means the kind of shear stress in an ideal gas somehow doesn't count in the Einstein equations, or if it means that it is not typically accounted for in "engineering" but does count in the Einstein equations?

Qmechanic
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mkcohen
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  • The momentum convective term is probably just due to the different definitions of the stress tensor. As discussed on the Wikipedia page for the stress tensor, there are a few different definitions. In General Relativity, the relevant stress tensor is the Hilbert one. In other areas of Physics, one often might use the canonical stress tensor, which often fails to be symmetric – Níckolas Alves Aug 29 '22 at 14:32
  • On the differences of perfect fluids and ideal gasses, see What's the difference between a perfect fluid and an ideal gas? – Níckolas Alves Aug 29 '22 at 14:34
  • This link should help: https://arxiv.org/abs/gr-qc/9812046v5 – KP99 Aug 29 '22 at 17:51
  • Note: in 3+1 formalism, as discussed in my above link, one can always express stress energy tensor of arbitrary source as that of a generic fluid. Only condition here is that topology of space- time is R×$\Sigma$ – KP99 Aug 29 '22 at 19:39
  • I'm afraid I couldn't figure out from that link. I searched for "ideal gas" and there were no results, and I looked at the section on perfect and imperfect fluids and couldn't figure out the answer to my question. Is there some reason there isn't a simple answer to how the tensor depends on the properties that completely describe an ideal gas (pressure, temperature, density)? – mkcohen Aug 30 '22 at 10:41

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