Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces

Abstract

Conditions for the existence of flows with non-null shear-free and expansion-free velocities in spaces with affine connections and metrics are found. On their basis, generalized Weyl's spaces with shear-free and expansion-free conformal Killing vectors as velocity's vectors of spinless test particles moving in a Weyl's space are considered. The necessary and sufficient conditions are found under which a free spinless test particle could move in spaces with affine connections and metrics on a curve described by means of an auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by the use of a dilaton field, the dilaton field appears as a scaling factor for the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv, 04.50.+h, 04.90.+e

20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv admin note: substantial text overlap with arXiv:gr-qc/0011045

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• Flows and particles with centrifugal (centripetal) and Coriolis' velocities and accelerations. Hubble's law in spaces with affine connections and metrics
• Centrifugal (centripetal) and Coriolis velocities and accelerations in spaces with affine connections and metrics as models of space-time