Relativistic transport theory for simple fluids at first order in the gradients: a stable picture

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called \textit{first order in the gradients} theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.Comment: 9 pages. Accepted in Physica

On the inertia of heat

Does heat have inertia? This question is at the core of a long-standing controversy on Eckart's dissipative relativistic hydrodynamics. Here I show that the troublesome inertial term in Eckart's heat flux arises only if one insists on defining thermal diffusivity as a spacetime constant. I argue that this is the most natural definition, and that all confusion disappears if one considers instead the space-dependent comoving diffusivity, in line with the fact that, in the presence of gravity, space is an inhomogeneous medium.Comment: 3 page