Abstract
In Denicol et al. [Phys. Rev. D 85, 114047 (2012)], the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in the Knudsen number, in the inverse Reynolds number, or their product. Terms of second order in the Knudsen number give rise to nonhyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in the inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scattering cross section. Consequently, we assess their relative importance in comparison to the terms which are of the order of the product of the Knudsen and inverse Reynolds numbers.
Highlights
AND CONCLUSIONSRelativistic fluid dynamics has found widespread applications in heavy-ion physics, in modeling nuclear collisions at ultrarelativistic bombarding energies [1,2], in astrophysics, for instance in modeling binary mergers of compact stellar objects, as well as in cosmology [4,5,6,7,8]
In order to solve the equations of motion of relativistic fluid dynamics, one has often made the assumption that the fluid is ideal, i.e., one demands instantaneous local thermodynamical equilibrium, which in turn allows to neglect all dissipative effects
A more realistic modeling of the dynamics of relativistic fluids demands that one uses the equations of relativistic dissipative fluid dynamics
Summary
Relativistic fluid dynamics has found widespread applications in heavy-ion physics, in modeling nuclear collisions at ultrarelativistic bombarding energies [1,2], in astrophysics, for instance in modeling binary mergers of compact stellar objects (see e.g. Ref. [3]), as well as in cosmology [4,5,6,7,8]. [24] a derivation of the equations of motion of relativistic dissipative fluid dynamics was presented, which is based on a systematic power-counting scheme in the Knudsen and inverse Reynolds number. The coefficients of terms involving gradients (or time derivatives) all have dimension of time (or mean-free path) and are proportional to the Knudsen number In this form, it is easy to apply power-counting arguments to estimate the order of magnitude of the various terms. We conclude that, in the 14moment approximation, for a massless Boltzmann gas, and for situations where the Knudsen and inverse Reynolds numbers are of the same order of magnitude, the equations of motion for the dissipative quantities read, to good approximation, as follows: τnn_ hμi þ nμ ≃ κ∇μα0 þ ðτnωμν − λnnσμνÞnν − δnnθnμ; (11).
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