Deviation equations of Synge and Schild over spaces with affine connections and metrics

Details Deviation equations of Synge and Schild over spaces with affine connections and metrics Deviation equations of Synge and Schild over spaces with affine connections and metrics

2000-12-05

arxiv.org/abs/gr-qc/0012015v1

Int.J.Mod.Phys. A16 (2001) 1109-1122

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTeX. To appear in Intern. J. Mod. Phys. A

Scientific paper

Deviation equation of Synge and Schild has been investigated over spaces with affine connections and metrics. It is shown that the condition for the vanishing of the Lie derivative of a vector field along a given non-null (non-isotropic) vector field u for obtaining this equation is only a sufficient (but not necessary) condition. By means of the vector field u and the projective metric (orthogonal to it) projected deviation equations of Synge and Schild have been obtained for a vector field, orthogonal to the given vector field u, as well as for the square of its length. For a given non-isotropic, auto-parallel and normalized vector field u this equation could have some simple solutions. PACS numbers: 02.90; 04.50+h; 04.90.+e: 04.30.+x

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