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This article is cited in 2 scientific papers (total in 2 papers)
Theoretical Physics
Gauge-invariant Tensors of 4-Manifold with Conformal Torsion-free Connection and their Applications for Modeling of Space-time
L. N. Krivonosova, V. A. Luk'yanovb a Nizhny Novgorod State Technical University, Nizhnii Novgorod, 603600, Russian Federation
b Zavolzhsk Branch of Nizhny Novgorod State Technical University, Zavolzhsk, Nizhegorodskaya obl., 606520, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
We calculated basic gauge-invariant tensors algebraically expressed through the matrix of conformal curvature. In particular, decomposition of the main tensor into gauge-invariant irreducible summands consists of 4 terms, one of which is determined by only one scalar. First, this scalar enters the Einstein's equations with cosmological term as a cosmological scalar. Second, metric being multiplied by this scalar becomes gauge invariant. Third, the geometric point, which is not gauge-invariant, after multiplying by the square root of this scalar becomes gauge-invariant object — a material point. Fourth, the equations of motion of the material point are exactly the same as in the general relativity, which allows us to identify the square root of this scalar with mass. Thus, we obtained an unexpected result: the cosmological scalar coincides with the square of the mass. Fifth, the cosmological scalar allows us to introduce the gauge-invariant 4-measure on the manifold. Using this measure, we introduce a new variational principle for the Einstein equations with cosmological term. The matrix of conformal curvature except the components of the main tensor contains other components. We found all basic gauge-invariant tensors, expressed in terms of these components. They are 1- or 3-valent. Einstein's equations are equivalent to the gauge invariance of one of these covectors. Therefore the conformal connection manifold, where Einstein's equations are satisfied, can be divided into 4 types according to the type of this covector: timelike, spacelike, light-like or zero.
Keywords:
conformal connection, gauge group, Einstein's equations, cosmological term.
Original article submitted 10/XII/2013 revision submitted – 21/II/2014
Citation:
L. N. Krivonosov, V. A. Luk'yanov, “Gauge-invariant Tensors of 4-Manifold with Conformal Torsion-free Connection and their Applications for Modeling of Space-time”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(35) (2014), 180–198
Linking options:
https://www.mathnet.ru/eng/vsgtu1291 https://www.mathnet.ru/eng/vsgtu/v135/p180
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