scholarly journals Teleparallel version of the Levi–Civita vacuum solutions and their energy contents

2008 ◽  
Vol 86 (9) ◽  
pp. 1091-1096 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Momentum Distribution ◽  
Radial Direction ◽  
Torsion Tensor ◽  
Axial Vector ◽  
Coupling Constant ◽  
Teleparallel Theory ◽  
Vacuum Solutions ◽  
Vector Part

In this paper, we find the teleparallel version of the Levi–Civita metric and obtain tetrad and the torsion fields. The tensor, vector, and the axial-vector parts of the torsion tensor are evaluated. It is found that the vector part lies along the radial direction only while the axial-vector vanishes everywhere because the metric is diagonal. Further, we use the teleparallel version of Moller, Einstein, Landau–Lifshitz, and Bergmann–Thomson prescriptions to find the energy-momentum distribution of this metric and compare the results with those already found in General Relativity (GR). It is worth mentioning here that momentum is constant in both of the theories for all the prescriptions. The energy in teleparallel theory is equal to the corresponding energy in GR only in the Moller prescription for the remaining prescriptions, the energy does not agree in both theories. We also conclude that Moller's energy-momentum distribution is independent of the coupling constant λ in the teleparallel theory.PACS Nos.: 04.20.–q, 04.20.Cv

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF STATIC AXIALLY SYMMETRIC SPACETIMES

2008 ◽  
Vol 23 (37) ◽  
pp. 3167-3177 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Momentum Distribution ◽  
Coupling Constant ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Comparison Of The Results ◽  
Special Case

This paper is devoted to discuss the energy–momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau–Lifshitz, Bergmann and Möller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of general relativity. It is mentioned here that Möller energy–momentum distribution is independent of the coupling constant λ. Finally, we calculate energy–momentum distribution for the Curzon metric, a special case of the above-mentioned spacetime.

scholarly journals Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity

2008 ◽  
Vol 86 (11) ◽  
pp. 1297-1302 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Spherical Shell ◽  
Momentum Density ◽  
Friedmann Universe ◽  
Coupling Constant ◽  
Dimensionless Coupling ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

A non-diagonal singularity-free model in torsion gravity

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Murat Korunur
Keyword(s):  
Radial Direction ◽  
Axial Vector ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Spin Effects ◽  
Dirac Particles ◽  
Free Model ◽  
Vector Part

AbstractIn the context of torsion (teleparallel) gravity, we focus on discussing the spin effects of Dirac particles associated with the non-diagonal singularity-free model (Mars space-time). We see that the vector part depends on the radial r and z directions and the axial-vector will be along the radial direction, that is, it will be symmetric about radial direction. Furthermore, the t = 0 case of the Mars metric is considered, thence it is seen that the axial-vector vanishes.

Dirac Spin and Angular Momentum of the Stationary Axisymmetric Space-Time in the Teleparallel Gravity

2020 ◽  
Author(s):  
M F Mourad
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Axial Vector ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Special Cases ◽  
Vector Part ◽  
Dirac Spin

In the framework of teleparallel equivalent to general relativity, the stationary axisymmetric space-time in the teleparallel gravity for two different sets of tetrad fields have been investigated. For these sets, we have obtained the expressions for the torsion vector, torsion axial-vector and the angular momentum of the solution. We found that the obtained expressions of the torsion axial-vector and the angular momentum are, in general quite different in both two sets of tetrad fields, while the expressions for the torsion vector have the same value. Moreover, the vector part connected with Dirac spin has been evaluated as well. Finally, special cases of the stationary axisymmetric space-time are discussed.

scholarly journals Teleparallel axions and cosmology

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Manuel Hohmann ◽  
Christian Pfeifer
Keyword(s):  
Dynamical System ◽  
General Relativity ◽  
Gauge Theories ◽  
Torsion Tensor ◽  
Scalar Fields ◽  
Field Equations ◽  
Axion Field ◽  
Teleparallel Theory ◽  
Pseudo Scalar ◽  
Scalar Invariants

AbstractWe consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields teleparallel axions. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.

Energy-momentum distribution in General Relativity and teleparallel theory of gravitation

2008 ◽  
Vol 86 (8) ◽  
pp. 985-993 ◽  
Author(s):  
M Sharif ◽  
K Nazir
Keyword(s):  
General Relativity ◽  
Energy Distribution ◽  
Momentum Distribution ◽  
Constant Energy ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

This paper investigates the energy-momentum distribution in General Relativity and the teleparallel theory of gravitation. We use Einstein, Landau–Lifshitz, Bergmann–Thomson, and Moller’s prescriptions in both the theories to evaluate the energy-momentum distribution of the Hiscock–Gott metric (inside and outside the stringlike object). It is shown that for outside the stringlike object, these energy-momentum complexes give a constant energy distribution in both theories. However, these turn out to be different inside the stringlike object. It is worth mentioning that both the theories give constant energy-momentum in all the prescriptions except for Moller’s inside and outside the stringlike object at large distances.PACS Nos.: 04.20.-q, 04.20.Cv

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