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

TL;DR

This paper investigates conditions for shear-free and expansion-free flows in affine connection spaces and Weyl's spaces, analyzing particle motion and the role of the dilaton field as a mass scale factor.

Contribution

It derives necessary and sufficient conditions for shear-free, expansion-free flows and particle trajectories in generalized Weyl's spaces with conformal Killing vectors.

Findings

Conditions for shear-free, expansion-free flows are established.

The motion of test particles along auto-parallel curves is characterized.

The dilaton field acts as a mass scaling factor in 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