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

S. Manoff·B. Dimitrov
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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

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S. Manoff, B. Dimitrov. 2000-11-30. Weyl's spaces with shear-free and expansion-free conformal Killing vectors and the motion of a free spinless test particle. https://arxiv.org/abs/gr-qc/0011045

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