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Register a new userHeat flux in the presence of a gravitational field in a simple dilute fluid: an approach based in general relativistic kinetic theory to first order in the gradients
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Added by
Alfredo Sandoval-Villalbazo
Publication date
2016
fields
Physics
and research's language is
English
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Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolmantextquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by textquotedblleft suppressingtextquotedblright{} the molecular acceleration in Boltzmanntextquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
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Transport properties in gases are significantly affected by temperature. In previous works it has been shown that when the thermal agitation in a gas is high enough, such that relativistic effects become relevant, heat dissipation is driven not solely by a temperature gradient but also by other vector forces. In the case of relativistic charged fluids, a heat flux is driven by an electrostatic field even in the single species case. The present work generalizes such result by considering also a magnetic field in an arbitrary inertial reference frame. The corresponding constitutive equation is explicitly obtained showing that both electric and magnetic forces contribute to thermal dissipation. This result may lead to relevant effects in plasma dynamics.
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.
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