On Hyperbolic “Theories” of Relativistic Dissipative Fluids

It is argued that, at least for the case of Navier-Stokes fluids, the so-called hyperbolic theories of dissipation are not viable. Consider a Navier-Stokes fluid. By this, we mean a substance that, within a certain regime, may be described as follows. First, the local state of the substance must be completely characterized, within this regime, by the values of precisely five fields on space-time: two scalar fields, ρ and n; two vector fields, u and q, the former unit timelike and the latter orthogonal to u; and one tensor field, τ, symmetric and also orthogonal to u. These fields are interpreted, respectively, as the fluid mass density, particle-number density, velocity, heat flow and stress. Second, the substance must be found to behave, within this regime, such that the following system of four equations [2] holds: ∇b((ρ+ p)u u + pg + 2qu + τ) = 0, (1)