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

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 f(T) gravity and energy distribution in Landau–Lifshitz prescription

2018 ◽  
Vol 27 (04) ◽  
pp. 1850039 ◽  
Author(s):  
M. G. Ganiou ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Energy Distribution ◽  
Cosmic String ◽  
Mass Formula ◽  
Plane Symmetric ◽  
Symmetric Metrics ◽  
Teleparallel Theory ◽  
Momentum Complex ◽  
Theory View

We investigate in this paper the Landau–Lifshitz energy distribution in the framework of [Formula: see text] theory view as a modified version of Teleparallel theory. From some important Teleparallel theory results on the localization of energy, our investigations generalize the Landau–Lifshitz prescription from the computation of the energy–momentum complex to the framework of [Formula: see text] gravity as it is done in the modified versions of General Relativity. We compute the energy density in the first step for three plane-symmetric metrics in vacuum. We find for the second metric that the energy density vanishes independently of [Formula: see text] models. We find that the Teleparallel Landau–Lifshitz energy–momentum complex formulations for these metrics are different from those obtained in General Relativity for the same metrics. Second, the calculations are performed for the cosmic string spacetime metric. It results that the energy distribution depends on the mass [Formula: see text] and the radius [Formula: see text] of cosmic string and it is strongly affected by the parameter of the considered quadratic and cubic [Formula: see text] models. Our investigation with this metric induces interesting results susceptible to be tested with some astrophysics hypothesis.

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF LEWIS–PAPAPETROU SPACETIMES

2007 ◽  
Vol 22 (06) ◽  
pp. 425-433 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
Energy Density ◽  
Momentum Distribution ◽  
Gravitational Effect ◽  
External Source ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Teleparallel Theory ◽  
Axisymmetric Solutions

In this paper, we find the energy–momentum distribution of stationary axisymmetric spacetimes in the context of teleparallel theory by using Möller prescription. The metric under consideration is the generalization of the Weyl metrics called the Lewis–Papapetrou metric. The class of stationary axisymmetric solutions of the Einstein field equations has been studied by Galtsov to include the gravitational effect of an external source. Such spacetimes are also astrophysically important as they describe the exterior of a body in equilibrium. The energy density turns out to be nonvanishing and well-defined and the momentum becomes constant except along θ-direction. It is interesting to mention that the results reduce to the already available results for the Weyl metrics when we take ω = 0.

Kerr–Newman solution in modified teleparallel theory of gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Azimuthal Angle ◽  
Polar Angle ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Square Root ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Teleparallel Theory ◽  
Theory Of Gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

scholarly journals Carter constant and angular momentum

2017 ◽  
Vol 27 (01) ◽  
pp. 1750180 ◽  
Author(s):  
Sajal Mukherjee ◽  
K. Rajesh Nayak
Keyword(s):  
Angular Momentum ◽  
Kerr Solution ◽  
Newtonian Mechanics ◽  
Axially Symmetric ◽  
Missing Link ◽  
Symmetric Spacetimes ◽  
Dipolar Potential ◽  
Carry Over ◽  
Definition Of ◽  
Special Case

We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between the Carter constant in stationary and axially symmetric spacetimes (SASS) such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic SASS.

scholarly journals Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
V. U. M. Rao ◽  
D. Neelima
Keyword(s):  
General Relativity ◽  
Bulk Viscosity ◽  
Space Time ◽  
Cosmological Models ◽  
Axially Symmetric ◽  
Matter Distribution ◽  
Field Equations ◽  
Theory Of Gravitation ◽  
The Universe ◽  
Special Case

Axially symmetric string cosmological models with bulk viscosity in Brans-Dicke (1961) and general relativity (GR) have been studied. The field equations have been solved by using the anisotropy feature of the universe in the axially symmetric space-time. Some important features of the models, thus obtained, have been discussed. We noticed that the presence of scalar field does not affect the geometry of the space-time but changes the matter distribution, and as a special case, it is always possible to obtain axially symmetric string cosmological model with bulk viscosity in general relativity.

scholarly journals QUANTUM GRAVITY IN PLEBANSKI FORMULATION

2011 ◽  
Vol 26 (31) ◽  
pp. 2323-2333
Author(s):  
L. V. LAPERASHVILI
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Gravitational Interaction ◽  
Graviton Mass ◽  
Coupling Constant ◽  
Independent Variables ◽  
Dimensionless Coupling ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant ◽  
Nonperturbative Theory

We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In Plebanski formulation of general relativity in which the tetrads, the connection and the curvature are all independent variables (and the usual relations among these quantities are valid only on-shell), we consider the nonperturbative theory of gravity with a nonzero background connection. We predict a tiny value of the graviton mass: mg≈1.5×10-42 GeV and extremely small dimensionless coupling constant of the perturbative gravitational interaction: g~10-60. We put forward the idea by Isimori56 on renormalizability of quantum gravity having multi-gravitons with masses m0, m1, …, mN-1.

AXIALLY SYMMETRIC SOLUTIONS IN DILATONIC THEORY AND THE SOLAR SYSTEM TESTS

1998 ◽  
Vol 13 (39) ◽  
pp. 3161-3167 ◽  
Author(s):  
TONATIUH MATOS ◽  
HUGO VILLEGAS ◽  
OCTAVIO OBREGÓN
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Symmetric Solution ◽  
Coupling Constant ◽  
Axially Symmetric

An analysis of the three classical solar system tests for dilatonic gravity coupled to electromagnetism is discussed using an exact, axially symmetric solution. At the post-Newtonian order there is no difference with general relativity, but a constraint on the coupling constant α is obtained at the next order.

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