Accelerator Seminar: Yaroslav Derbenev - The Issues of Geodesics and Torsion in the Theory of Gravitation

Title: To the Issue of Geodesics and Torsion in the Theory of Gravitation



A simple differential analysis of the issue of correspondence between notion of the geodesics in gravitation theory of GTR and straights of inertial motion in the Minkowski’ space-time discovers that, conventional certification of the geodesics in GTR is not compatible with the existence of the Riemann-Christoffel curvature tensor (RCT). We show that, a resolution of this crisis consists of a natural extension of the Christoffels in the dynamic law to general connectedness form including a triadic asymmetric tensor (named the moderator). The correspondent Riemann supertensor form, unavoidably annihilating by certification of the moderate geodesics, gives birth to torsion (skew-symmetric part of the moderator) and the gravitensor (the even-symmetric part); both arrive as a functional of the RCT and become an indispensable integral part of structure of the gravitational field. The equivalence principle still actual while becomes enriched in the content. The Einstein-Hilbert law of the metric to matter connection remains unchanged at the produced correction of the gravitational dynamics. The produced completion of the connectedness leads also to a renormalization of the dynamical metric and spin precession in gravitation field. We pay attention to possible implication of the torsion in the elementary interactions.