Torsion Axial-Vector and Gravitational Energy for a Stiff Fluid Model in the Theory of Teleparallel Gravity

2013 ◽  
Vol 53 (1) ◽  
pp. 307-319
Author(s):  
Ragab M. Gad
Keyword(s):  
Fluid Model ◽  
Axial Vector ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Stiff Fluid

scholarly journals The Chaplygin gas as a model for modified teleparallel gravity?

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Shambel Sahlu ◽  
Joseph Ntahompagaze ◽  
Maye Elmardi ◽  
Amare Abebe
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Fluid Model ◽  
State Parameter ◽  
Teleparallel Gravity ◽  
Chaplygin Gas ◽  
Stiff Fluid ◽  
Fluid Systems ◽  
Equation Of State Parameter ◽  
Lagrangian Densities

Abstract This paper explores the possibility of treating the exotic Chaplygin-gas (CG) fluid model as some manifestation of an f(T) gravitation. To this end, we use the different cosmological CG equations of state, compare them with the equation of state for the modified teleparallel gravity and reconstruct the corresponding Lagrangian densities. We then explicitly derive the equation of state parameter of the torsion fluid $$w_T$$wT and study its evolution for vacuum-torsion, radiation-torsion, dust-torsion, stiff fluid-torsion and radiation-dust-torsion multi-fluid systems. The obtained Lagrangians have, in general, matter dependence due to the matter-torsion coupling appearing in the energy density and pressure terms of the modified teleparallel gravity theory. For the simplest CG models, however, it is possibly to reconstruct f(T) Lagrangians that depend explicitly on the torsion scalar T only. The preliminary results show that, in addition to providing Chaplygin-gas-like solutions to the modified teleparallel gravitation, which naturally behave like dark matter and dark energy at early and late times respectively, the technique can be used to overcome some of the challenges attributed to the CG cosmological alternative.

scholarly journals THE GRAVITATIONAL ENERGY PROBLEM FOR COSMOLOGICAL MODELS IN TELEPARALLEL GRAVITY

2010 ◽  
Vol 19 (12) ◽  
pp. 1925-1935 ◽  
Author(s):  
S. C. ULHOA ◽  
J. F. DA ROCHA NETO ◽  
J. W. MALUF
Keyword(s):  
Average Energy ◽  
Teleparallel Gravity ◽  
Space Time ◽  
Gravitational Energy ◽  
Cosmological Models ◽  
De Sitter ◽  
Energy Problem ◽  
First Case ◽  
Einstein's Equation ◽  
Average Energy Density

We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space–time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild–de Sitter solution of Einstein's equation, and then to the Robertson–Walker universe. We show that in the first case our method leads to an average energy density of the vacuum space–time, and in the latter case the energy vanishes in the case of null curvature.

MAXWELL FIELDS IN ANISOTROPIC SPACETIMES

1998 ◽  
Vol 07 (05) ◽  
pp. 749-771 ◽  
Author(s):  
MATTHIAS WOLLENSAK
Keyword(s):  
Bianchi Type ◽  
Fluid Model ◽  
Analytic Solutions ◽  
Type I ◽  
Time Behavior ◽  
Stiff Fluid ◽  
Transversality Conditions ◽  
Maxwell Fields ◽  
Bianchi Type I Universe ◽  
Short Time

Maxwell's equations are rewritten with respect to anholonomic orthonormal frames and applied to the case when the background is described by a diagonal Bianchi Type I universe with line element [Formula: see text]. It is generally shown that solutions analogous to plane wave solutions in flat spacetime must obey two transversality conditions when the spacetime is anisotropic i.e., when at least one of the coefficients αj(t) differs from the others. Analytic solutions are presented for propagation along the respective coordinate axes and a special stiff fluid model. Furthermore, by use of a generally applicable ansatz the long- and short-time behavior of waves traveling in the axisymmetric Kasner universe have been investigated.

scholarly journals TELEPARALLEL GRAVITATIONAL ENERGY IN THE GAMMA METRIC

2006 ◽  
Vol 15 (05) ◽  
pp. 695-701 ◽  
Author(s):  
MUSTAFA SALTI
Keyword(s):  
General Relativity ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Coupling Constants ◽  
Dimensionless Coupling ◽  
Weinberg Complex

The Møller energy (due to matter and fields including gravity) distribution of the gamma metric is studied in teleparallel gravity. The result is the same as those obtained in general relativity by Virbhadra in the Weinberg complex and Yang–Radincshi in the Møller definition. Our result is also independent of the three teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.

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.

TORSION VECTOR AND TORSION AXIAL-VECTOR IN VAN STOCKUM SPACETIME

2012 ◽  
Vol 27 (18) ◽  
pp. 1250099
Author(s):  
RAGAB M. GAD
Keyword(s):  
Axial Vector ◽  
Teleparallel Gravity ◽  
Dirac Particle ◽  
Spin Precession ◽  
Tetrad Field

In this paper, we work with teleparallel gravity and show that the values of the torsion vector and the torsion axial-vector depend on the choice of the tetrad field. We choose two different sets of tetrad fields, each of them satisfies the tetrad's conditions and leads to the Van Stockum spacetime. We obtain expressions for the torsion vector and the torsion axial-vector. In addition, we found that the obtained expressions are quite different for the two sets of tetrad fields. For the spacetime under consideration, if the metric coefficients are assumed to be functions of t only, it is then shown that the torsion axial-vector vanishes completely and the torsion vector still depends on the choice of tetrad fields. Finally, we found the spin precession of a Dirac particle in the spacetime under consideration.

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.

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