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?
