A Generalized Fermi Derivative and Dissipative Gas Dynamics Equations

Authors: Söderholm,  L. H. S.
Document Type: Article
Pubstate: Published
Journal: Class. Quantum Grav.
Volume: 16   2225-9
Year: 1999


A generalized Fermi derivative associated with the relativistic flow of a continuum is introduced. The derivatives of the metric tensor and the four-velocity field vanish. The corresponding transport is non-rotating. The derivative has torsion. When taken along a world-line 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 four-velocity. The derivative commutes with the projection operators associated with the four-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.