Hi,

I think it is not the question of physics of fluids but it is the question of mathematical models we use. For example, let's take ordinary water. At everyday life timescale, it is well approximated by Newton's law of viscosity. But at time scales of the order of GHz Newton's viscous law does not work and we should say that water is viscoelastic. However, at shorter timescales, water behaves like an elastic solid, e.g. see Article Two liquid states of matter: A dynamic line on a phase diagram

So what is water - Newtonian fluid, viscoelastic fluid or elastic solid?

In reality, there are no pure viscous, elastic or viscoelastic media. It is just the question of the observation timescale.

In relativistic fluid dynamics, we also might be interested in different timescales, short and long. But the fact is that the mathematical form of the famous Navier-Stokes equations with which we used to approximate fluids does not work in relativistic settings because of the intrinsic acausal behavior of the solution. It is well known that the Laplace operator in the viscous part gives the superluminal velocity of signal propagation (related to shear modes). This basically makes the N-S unusable in the relativistic settings because of the contradiction with physics but also because the initial value problem for the relativistic N-S is ill-posed.

It is not the question of physics but the question of mathematical approximation.

The intrinsic defect of the Newton law of viscosity (in the relativistic context) is that it is a steady-state law. It ignores the unsteady process during which this steady state was achieved. This means that it kills the internal time scale which is related to the dissipation of the shear modes.

The relativistic reality is such that you can not ignore this timescale even though your timescale of interest is of several orders of magnitude longer. Otherwise, you end up with an acausal behavior and ill-posedness.

Usually, people indeed use Israel-Stewart-type equations which keep this timescale related to dissipation of shear modes. However, I think, it is applicable only to rarified gases and can't be applied to dense objects like neutron stars for example. We are developing an alternative geometrical approach which treats matter (either fluid or solid) as a Riemann-Cartan manifold. It seems that it is applicable to all three states of matter: gaseous, liquid and solid. See preliminary results in this presentation

Presentation General relativistic formulation of dissipative continuum mechanics

Ilya

Thanks a lot.