Gravity and spin with a nonsymmetric metric tensor

Hammond, Richard T.

doi:10.1007/s10714-019-2572-8

Cited by 3 publications

(2 citation statements)

References 30 publications

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“…Gauge covariant generalizations are discussed in [49] and an extended conformal invariance and non-metricity are found in [50,51]. Nonsymmetric metric tensor has been used then to explore gravity and spin [52]. The metric and connection as fundamental quantities to form the spacetime have been constructed in a Weyl-invariant way [53].…”

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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“…Gauge covariant generalizations are discussed in [48] and an extended conformal invariance and non-metricity are found in [49]. Nonsymmetric metric tensor has been used then to explore gravity and spin [50]. The Einstein-Hilbert theory itself was obtained as an effective theory due to quantum corrections of torsion with the conjecture that torsion is of intrinsic quantum nature [51].…”

Section: Introductionmentioning

confidence: 99%

Consistent solution of Einstein-Cartan equations with torsion outside matter

Morawetz

2020

Preprint

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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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Gravitational dipole moment from an exact solution with torsion

Hammond

2020

New J. Phys.

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Dipole fields are common in electromagnetism and may be viewed as the result of a positive and negative charge (or pole) which are close together. A dipole field in gravity is not expected to exist because negative mass has never been observed. However, an exact solution to the gravitational field equations with torsion is presented that does correspond to a dipole gravitational field, even though there is no negative mass. The theory is based on a non-symmetric metric tensor, and it is found there is a singularity in the metric tensor at the origin but no event horizon. Gravitational dipoles have been used to solve the dark matter problem.

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Gravity and spin with a nonsymmetric metric tensor

Cited by 3 publications

References 30 publications

Consistent solution of Einstein–Cartan equations with torsion outside matter

Consistent solution of Einstein–Cartan equations with torsion outside matter

Consistent solution of Einstein-Cartan equations with torsion outside matter

Gravitational dipole moment from an exact solution with torsion

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