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

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.

CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR PROPER TELEPARALLEL HOMOTHETIC VECTOR FIELDS IN THE TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (25) ◽  
pp. 2145-2153 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Special Choice ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

In this paper we explored teleparallel homothetic vector fields in Bianchi type I spacetimes in the teleparallel theory of gravitation using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11 which are same in numbers as in general relativity. In the cases of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice of the spacetimes. In the case of 11 teleparallel homothetic vector fields all the torsion components are zero. The homothetic vector fields of general relativity are recovered in this case and the spacetime become Minkowski.

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.

CLASSIFICATION OF CYLINDRICALLY SYMMETRIC STATIC SPACETIMES ACCORDING TO THEIR KILLING VECTOR FIELDS IN TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (07) ◽  
pp. 525-533 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Minkowski Spacetime ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Cylindrically Symmetric ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

In this paper we classify cylindrically symmetric static spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of r. In the case of 10 Killing vector fields the spacetime becomes Minkowski spacetime and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. It is important to note that this classification also covers the plane symmetric static spacetimes.

scholarly journals MØLLER ENERGY–MOMENTUM PRESCRIPTION FOR A LOCALLY ROTATIONALLY SYMMETRIC SPACE–TIME

2006 ◽  
Vol 21 (18) ◽  
pp. 3845-3853 ◽  
Author(s):  
OKTAY AYDOGDU
Keyword(s):  
General Relativity ◽  
Energy Distribution ◽  
Bianchi Type ◽  
Space Time ◽  
Type Ii ◽  
Theory Of Relativity ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric ◽  
Teleparallel Theory ◽  
The Universe

The energy distribution in the Locally Rotationally Symmetric (LRS) Bianchi type II space–time is obtained by considering the Møller energy–momentum definition in both Einstein's theory of general relativity and teleparallel theory of relativity. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, and Aydogdu and Salti. Our result — the total energy of the universe is zero — supports the view points of Albrow and Tryon.

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

A NOTE ON KILLING VECTOR FIELDS OF BIANCHI TYPE II SPACETIMES IN TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (20) ◽  
pp. 1733-1740 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type Ii ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

The aim of this paper is to classify Bianchi type II spacetimes according to their teleparallel Killing vector fields using the direct integration technique. Studying teleparallel Killing vector fields in the above spacetimes, it turns out that the dimensions of the teleparallel Killing vector fields are 4, 5 or 7. A brief comparison between teleparallel and general relativity Killing vector fields are given. It is shown that for the above spacetimes in the presence of torsion we get more conservation laws which are different from the theory of general relativity.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

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