To the issue of Geodesics and Torsion in Riemannian geometry and Theory of the Gravitation: analysis of consistence and update of the conventional concept

Yaroslav Derbenev

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arXiv · 2304.14223

To the issue of Geodesics and Torsion in Riemannian geometry and Theory of the Gravitation: analysis of consistence and update of the conventional concept

Yaroslav Derbenev

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Abstract

A simple differential analysis of issue of the correspondence between notion of 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, resolution of the contradiction consists of a natural extension of the Christoffel symbols in the gravitation dynamic law to the complete connectedness form which includes a triadic asymmetric tensor (named the moderator). The correspondent Riemann supertensor form, unavoidably annihilating by certification of 4-vectors of particle momentum and spin, gives birth to torsion (skew-symmetric part of the moderator) and the gravitensor (the even-symmetric part); both arrive connected to the RCT and become an indispensable integral part of structure of the gravitational field. The equivalence principle still actual while it 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. Our analysis results in the gravitensor addition to Christoffels in equation for geodesics, modified equations for 4-vector of particle spin with contribution from torsion, and renormalization of metric in the update dynamic concept of the GTR. We pay attention to possible implication of torsion in the elementary interactions.

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Yaroslav Derbenev. 2023-04-27. To the issue of Geodesics and Torsion in Riemannian geometry and Theory of the Gravitation: analysis of consistence and update of the conventional concept. https://arxiv.org/abs/2304.14223

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