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14.4 Remaining issues

We have discussed some of the models that have been constructed in order to incorporate dissipative effects in a relativistic fluid description. We have seen that the most obvious ways of doing this, the “text-book” approach of Eckart [39] and Landau and Lifshitz [66], fail completely. They do not respect causality and have serious stability problems. We have also described how this problem can be fixed by introducing additional dynamical fields. We discussed the formulations of Israel and Stewart [1075758] and Carter [20] in detail. From our discussion it should be clear that these models are examples of an extremely large family of possible theories for dissipative relativistic fluids. Given this wealth of possibilities, can we hope to find the “right” model? To some extent, the answer to this question relies on the extra parameters one has introduced in the theory. Can they be constrained by observations? This question has been discussed by Geroch [47] and Lindblom [73]. The answer seems to be no, we should not expect to be able to use observations to single out a preferred theoretical description. The reason for this is that the different models relax to the Navier–Stokes form on very short timescales. Hence, one will likely only be able to constrain the standard shear and bulk viscosity coefficients, etc. Related questions concern the practicality of the different proposed schemes. To a certain extent, this is probably a matter of taste. Of course, it may well be that the additional parameters required in a particular model are easier to extract from microphysics arguments. This could make this description easier to use in practice, which would be strong motivation for preferring it. Of course, there is no guarantee that the same formulation will be ideal for all circumstances. Clearly, there is scope for a lot more research in this problem area.


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