Relativistic transport theory for simple fluids to first order in the gradients

Abstract

a b s t r a c tIn this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be cast 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 ''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.

Jeans instability analysis in the presence of heat in Eckart’s frame

“…[7] regarding first order theories [10]. The question here is whether such instabilities are removed when the effects of gravitational fields are included in the calculation [11][12][13]. In the present work we show that the inclusion of such fields, together with the heat-acceleration coupling in the framework of relativistic hydrodynamics still yields a pathological behavior regarding the observed characteristic times in which gravitational collapse takes place.…”

Remarks on relativistic kinetic theory to first order in the gradients

“…(1) comes from the fact that it is inconsistent with classical irreversible thermodynamics in two senses: it does not have the structure given by Eq. (8) and it leads to a violation of the linear regression of fluctuations hypothesis. The proof of this last statement follows directly from the fluctuation analysis using standard hydrodynamics techniques.…”

Heat conduction in relativistic neutral gases revisited

“…The positive root of that equation, in Fourier-Laplace space, leads to an exponential growth of fluctuations with a very small characteristic time. However, when the Boltmzann equation is solved by means of the Chapman-Enskog method for the (special) relativistic simple gas, the constitutive equation obtained couples the heat flux with gradients of the state variables [4][5][6][7]. In that case the differential equation for the transverse velocity mode turns out to be first order and leads to an exponential decay of fluctuations [7,8].…”