2000/05/10 by Sawa Manoff, S. Manoff, Manoff, S.
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0005027
35 pages
arxiv created 2000/05/10 · openalex publication_date 2000/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The influence of the torsion on the relative velocity and on the relative acceleration between particles (points) in spaces with an affine connection and a metric [(Ln,g)-spaces] and in (pseudo) Riemannian spaces with torsion (Un-spaces) is considered. Necessary and sufficient conditions as well as only necessary and only sufficient conditions for vanishing deformation, shear, rotation and expansion are found. The notion of relative acceleration and the related to it notions of shear, rotation and expansion accelerations induced by the torsion are determined. It is shown that the kinematic characteristics induced by the torsion (shear acceleration, rotation acceleration and expansion acceleration) could play the same role as the kinematic characteristics induced by the curvature and can (under given conditions) compensate their action as well as the action of external forces. The change of the rate of change of the length of a deviation vector field is given in explicit form for (Ln,g)- and Un-spaces. PACS numbers: 04.90+e, 04.50+h, 12.10.Gq, 03.40.-t