A generalized Fermi derivative and dissipative gas dynamics equations

Physics

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Scientific paper

A generalized Fermi derivative associated with the relativistic flow of a continuum is introduced. The derivatives of the metric tensor and the 4-velocity field vanish. The corresponding transport is non-rotating. The derivative has torsion. When taken along a worldline of the continuum, the derivative reduces to the well known Fermi derivative, connected with Fermi-Walker propagation. The vanishing of the generalized Fermi derivative of a vector along a curve implies that the vector is boosted with the 4-velocity. The derivative commutes with the projection operators associated with the 4-velocity field. The 14-moments dissipative gas dynamic equations of Israel and Stewart (besides the equations of conservation of mass and energy-momentum) are formulated in terms of the generalized Fermi derivative and combined into one single equation for the dissipative part of the energy-momentum tensor.

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