Relativistic transport theory for simple fluids at first order in the gradients: a stable picture
arXiv:0805.4237 · doi:10.1016/j.physa.2009.06.001
Abstract
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.
arXiv comment9 pages. Accepted in Physica A
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Cited by in corpus (13)
- Relativistic Fluid Dynamics: Physics for Many Different Scales
- Relativistic fluid dynamics: physics for many different scales
- An introduction to the relativistic kinetic theory on curved spacetimes
- A consistent first-order model for relativistic heat flow
- Heat conduction in relativistic neutral gases revisited
- Tolman's law in linear irreversible thermodynamics: a kinetic theory approach
- Generic instabilities in the relativistic Chapman-Enskog heat conduction law
- Remarks on relativistic kinetic theory to first order in the gradients
- Jeans instability analysis in the presence of heat in Eckart's frame
- On the stability problem in relativistic thermodynamics: implications of the Chapman-Enskog formalism
- On the inertia of heat
- Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable first order in the gradients formalism
- The energy-momentum tensor in relativistic kinetic theory: the role of the center of mass velocity in the transport equations for multicomponent mixtures