A ug 1 99 5 The Relaxation Effect in Dissipative Relativistic Fluid Theories

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple rel-ativistic Navier-Stokes descriptions of these states. Thus, for example, in the relaxed form of a physical fluid state the stress energy tensor is in effect indistinguishable from a perfect fluid stress tensor plus small dissipative corrections proportional to the shear of the fluid velocity, the gradient of the temperature, etc. §I Introduction A simple mathematical model provides an elegant and accurate description of the common materials called fluids. The effects of internal dissipation in these materials— viscosity and thermal conductivity—are also well modeled by a simple generalization of the basic theory called the Navier-Stokes equations. Unfortunately, the most straightforward approaches to constructing relativistic generalizations of the Navier-Stokes equations result in rather pathological theories (Eckart [1], Landau and Lifschitz [2]). These theories are non-causal, unstable, and without a well posed initial value formulation (see for example Hiscock and Lindblom [3]). Less straightforward approaches have succeeded more recently in producing a class of causal dissipative fluid theories (e. These theories have eliminated the pathologies of the straightforward relativistic generalizations of the Navier-Stokes equations, but they do so at the expense of increasing significantly the number of dynamical fields needed to describe the fluid. Unfortunately the additional dynamical degrees of freedom associated with these extra fields have never been directly observed in real fluids. This is probably why these new theories have not found widespread acceptance. In this paper the dynamics associated with these additional fluid fields are analyzed in a very large class of causal dissipative fluid theories. It is shown that the physical fluid states relax (on a time scale characteristic of the inter-particle interactions) to ones that are also well described by the simple relativistic Navier-Stokes theory. For example, the stress-energy tensor in such a relaxed fluid state is well described by the usual perfect fluid stress-energy tensor plus the Navier-Stokes expressions for the dissipative corrections involving the shear of the fluid velocity, the gradient of the temperature, etc. This result suggests that meaningful differences between the causal theories and the non-causal Navier-Stokes theory can not be observed. The complicated dynamical structure of the causal