Weyl's spaces with shear-free and expansion-free conformal Killing vectors and the motion of a free spinless test particle

Abstract

Conditions for the existence of shear-free and expansion-free non-null vector fields in spaces with affine connections and metrics are found. On their basis Weyl's spaces with shear-free and expansion-free conformal Killing vectors 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

arXiv comment21 pages, LaTeX. The title is squeezed. Some typos and explanations are removed. New references are added and all references are written in the form required by Classical and Quantum Gravity

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