Some structural features induced by the space-time metrical fluctuation in the theory of gravitational fields

Abstract

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg _λκ (x)=g_λκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT ^λμ_κ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT ^λμ_κ (i.e.,T ^λμ_κ =δ ^λ_κ σ_μ−δ ^μ_κ σ_λ(σ_μ=∂σ/∂x ^μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT ^λμ_κ .