The use of symbolic calculations in post-Riemannian and multidimensional theories of gravity

Babourova, O. V.; Kostkin, R. S.; Frolov, B. N.

doi:10.1134/s0202289311040025

Cited by 3 publications

(5 citation statements)

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“…Weyl's geometry can be extended naturally to include torsion. The corresponding geometry is called the Weyl-Cartan geometry, and it was extensively studied from both physical and mathematical points of view [43][44][45][46][47][48][49][50][51]. For a review of the geometric properties and of the physical applications and of the Riemann-Cartan and Weyl-Cartan space-times see [52].…”

Section: Introductionmentioning

confidence: 99%

Weyl type f(Q, T) gravity, and its cosmological implications

et al. 2020

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We consider an f(Q, T) type gravity model in which the scalar non-metricity $$Q_{\alpha \mu \nu }$$Qαμν of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $$w_{\mu }$$wμ. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), and we compare the predictions of the theory with the standard $$\Lambda $$ΛCDM model.

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Section: Introductionmentioning

confidence: 99%

Weyl type f(Q, T) gravity, and its cosmological implications

et al. 2020

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“…It is worth mentioning again that the effect of the nonminimal matter-geometry coupling f (Q, T ) will enter into the Raychaudhury equation (63) through the expression of the extra force, given by Eq. (44).…”

Section: Generalized Raychaudhuri Equation In Weyl-type F ( Q T ) Theorymentioning

confidence: 99%

“…In an important mathematical and physical development Cartan introduced the anti-symmetric part of the connection, known as torsion, into the gravity theory, thus formulating an extension of GR [54], which is known as the Einstein-Cartan theory. The Weyl geometry can be immediately generalized by including the torsion, which leads to the Weyl-Cartan geometry, and a corresponding geometric theory of gravitation [55][56][57][58][59][60][61][62][63][64][65][66]. For a review of geometrical properties and physical applications of Riemann-Cartan and Weyl-Cartan spacetimes one can refer to [67].…”

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confidence: 99%

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T) gravity

et al. 2021

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We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl-type f(Q, T) gravity, in which the non-metricity Q is represented in the standard Weyl form, fully determined by the Weyl vector, while T represents the trace of the matter energy–momentum tensor. The effects of the Weyl geometry and of the extra force induced by the non-metricity–matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the non-metricity–matter coupling, are obtained in the weak-field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl-type f(Q, T) gravity.

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“…It leads to a redefinition of other geometric quantities of the theory. Resulting from this procedure is a conformal theory of gravity in the Weyl-Cartan spacetime [18]- [20] with an additional geometric structure of the Dirac's scalar field β, which in this approach arises naturally as a necessary element of the theory. In other theories, which dealt with the scalar field in affine-metric theory of gravity [21], [22], this field is introduced into the theory from the outside "by hands", which is rather artificial.…”

Section: Introductionmentioning

confidence: 99%

“…In contradiction with this, we do not reject the inflation and the Λ-term. In [18]- [20] we have expressed the hypothesis that the dark energy is determined by the value of the Dirac scalar field via the term Λ 0 β 4 of the Lagrangian. The conformal theory with a scalar field in the Weyl-Cartan spacetime that is developed in the paper proposed is wider than the theory developed in [23]- [26] because it contains (in comparison with that) two additional geometrical quantities -the Weyl vector and the torsion tensor.…”

Section: Introductionmentioning

confidence: 99%