Теорія гравітації в афінному репері
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 1
Abstract
THEORY OF GRAVITY IN AFFINE RAPPER Samokhvalov S.E., Krikent A.I. Abstract The article deals with the affine metric theory of gravitation. The gravitational field is determined by the curvature (geodesic deviation) and should not depend on the method of the curvature describing. So, the discussion what is more important in the theory of gravity - general covariance or will in the choice of reference fields - unfounded [1]. The theory must be invariant as relatively general covariant transformations and relative changes that associated with the choice of an arbitrary affine rapper. This transformation, involving active approach (rather than passive relating to the choice of different ways of numbering) can be provided the physical sense - motion in the gravitational field and the transition between systems of reference. It can be also link the transition between systems of reference when choosing the reference (holonomic) field as the coordinate reference system with generally covariant transformations. There are several approaches to describe the phenomenon of gravity. For example, the theory of gravity in orthonormal rapper was built as a gauge theory of translations [2], thus the equation of the gravitational field were presented in the form that is similar to the form of dynamic equations of Maxwell, according to which an electric current is shown as the divergence antisymmetric tensor of the electromagnetic field, that is quasilocal. It was also found [3] that the currents of any physical quantities stored due gauge symmetries are quasi that is expressed through superpotentsial. As an example the superpotentsial of energy-momentum of gravitational field in the coordinate frames was built. The paper presents the general theory of relativity in arbitrary affine rappers, shows the Lagrangian theory L g ( ) c a b a b c c b b a a c c d a c bd ab 2 1 2 1 and equations of motion, where the components of affine frame are used as main variables, and also given the expression systems of energy-momentum and the suitable superpotentsial a a S eB . References [1] Rodychev V.Y. Teoryya tyahotenyya v ortohonalnom repere. – M.: Nauka, 1974. – 184 s. [2] Samokhvalov S.E. & Vanyashin V.S. (1991). Group theory approach to unification of gravity with internal symmetry gauge interactions. Class. Quantum Grav., V. 8, P. 2277-2282. [3] Samokhvalov S.E. Teoretyko-hrupove pidgruntya holohrafichnoho pryntsypu // Matematychne modelyuvannya. – 2010. – №2(23). – S. 7-11.
Authors and Affiliations
С. Є. Самохвалов, А. І. Крикент
Keywords
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