Relativistic hydrodynamics – causality and stability

Abstract

Abstract. Causality and stability in relativistic dissipative hydrodynamics are important conceptual issues. We argue that causality is not restricted to hyperbolic set of differential equations. E.g. heat conduction equation can be causal considering the physical validity of the theory. Furthermore we propose a new concept of relativistic internal energy that clearly separates the dissipative and non-dissipative effects. We prove that with this choice we remove all known instabilities of the linear response approximation of viscous and heat conducting relativistic fluids. In this paper the Eckart choice of the velocity field is applied.

Galilean relativistic fluid mechanics

“…This approach to thermodynamics is also a benchmark, a tool of verification of a thermodynamic theory. In case of Galilean relativistic fluids we expect, that the homogeneous equilibrium be asymptotically stable without any additional conditions beyond the thermodynamic requirements [96,67]. For classical fluids the following statement can be proved:…”

“…-The main motivation of this work comes from our attempts to clarify the relation of generic stability, thermodynamics and flow-frames in dissipative relativistic fluids: [96,97,98,67,99,71,85,86,68,87].…”

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

“…From our point of view it is interesting to observe that (at least some) remedies proposed to improve the formulation of -hydrodynamic [64,65,70,71] (like the use of some induced memory effects) introduce conditions which in statistical physics lead in a natural way to its nonextensive version described by the parameter [22][23][24][25][26][27][28]. It is then natural to expect that a nonextensive version of the hydrodynamical model with the nonextensivity parameter could help us to circumvent (at least to some extent) the problems mentioned.…”

“…However, one needs their special relativistic generalization and this turns out to be acausal and unstable [64,65] (see also [66][67][68][69][70][71]). One therefore looks towards the extended, second order theories accepting all problems connected with their formulation and practical applications [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87].…”

“…(1) we are, in fact, assuming that, instead of a strict (local) equilibrium, a kind of stationary state is being formed, which already includes some interactions and which is summarily characterized by a parameter ; very much in the spirit of [54][55][56][57][58][59][60] mentioned before. With this assumption we are already departing from the picture of the usual ideal fluid with its local thermal equilibrium, which is the prerogative of ideal hydrodynamics [64,65]. The consequences of this fact will be discussed below.…”