Axially Symmetric Solution of the Weyl–Cartan Theory of Gravity and the Problem of the Rotation Curves of Galaxies

Babourova, O. V.; Kudlaev, P. E.; Frolov, B. N.

doi:10.1007/s11182-016-0910-9

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Consequently, the dynamics of metric-affine gravity with torsion is discussed in [76]. However, there are reports about the metric of the axially symmetric solution [77,78] in empty space and its application to the rotation curves of spiral galaxies [77]. It was found that the vacuum torsion interacts with spin momenta of astrophysical objects which can lead to modifications of Newton's law [78].…”

Section: Introductionmentioning

confidence: 99%

Consistent solution of Einstein–Cartan equations with torsion outside matter

Morawetz

2021

Class. Quantum Grav.

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The Einstein–Cartan equations in first-order action of torsion are considered. From Belinfante–Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer–Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman–Lamaître–Robertson–Walker cosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type.

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Section: Introductionmentioning

confidence: 99%

Consistent solution of Einstein–Cartan equations with torsion outside matter

Morawetz

2021

Class. Quantum Grav.

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“…A special case of a general affine-metric space is a Cartan-Weyl space in which the nonmetricity is bounded by the Weyl condition. The Cartan-Weyl space is used, for example, in the theory of Weyl-Dirac gravity [3,4].…”

Section: Introductionmentioning

confidence: 99%

Structure of plane gravitational waves of nonmetricity in affine-metric space

Babourova

Frolov

Khetseva

et al. 2018

Class. Quantum Grav.

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A definition of an affine-metric space of the plane wave type is given using the analogy with the properties of plane electromagnetic waves in Minkowski space. The action of the Lie derivative on the 40 components of the nonmetricity 1-form in the 4-dimensional affine-metric space leads to the conclusion that the nonmetricity of a plane wave type is determined by five arbitrary functions of delayed time. A theorem is proved that parts of the nonmetricity 1-form irreducible with respect to the Lorentz transformations of the tangent space, such as the Weyl 1-form, the trace 1-form, and the spin 3 1-form, are defined by one arbitrary function each, and the spin 2 1-form is defined by two arbitrary functions. This proves the possibility of transmitting information with the help of nonmetricity waves.

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