Both are important differences. But many results from the non-relativistic theory will remain formally valid.
Thus for instance in the relativistic case we still haveis in the class of moments. In fact is equal to the four-velocity of the gas to within a factor. We have
We recall the discussion – in Section 4.2 – of the important role played by in ensuring symmetric hyperbolicity of the field equations: Symmetric hyperbolicity was due to the concavity of in the privileged frame moving with the four-velocity . Now we see from (72) that – for the non-degenerate gas – we have so that the privileged frame is the local rest frame of the gas. This is quite satisfactory, since the rest frame is naturally privileged. [There remains the question of why the rest frame is not the privileged one for a degenerate gas. This point is open and invites investigation.]
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