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

TL;DR

This paper investigates the geometric conditions for shear-free, expansion-free vector fields in affine connection spaces, explores Weyl's spaces with conformal Killing vectors, and analyzes the motion of free test particles influenced by the dilaton field.

Contribution

It derives necessary and sufficient conditions for shear-free, expansion-free vector fields and examines test particle motion in Weyl's spaces with dilaton fields affecting mass density.

Findings

Conditions for shear-free, expansion-free vector fields established.

Weyl's spaces with conformal Killing vectors characterized.

Dilaton field influences test particle mass scaling.

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