Energy and Momentum Densities of Cosmological Models, with Equation of State rho= mu, in General Relativity and Teleparallel Gravity (original) (raw)
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International Journal of Theoretical Physics, 2007
We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energymomentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.
Energy contents of some non-vacuum spacetimes in teleparallel gravity
Astrophysics and Space Science, 2010
This paper elaborates the problem of energy-momentum in the framework of teleparallel equivalent of General Relativity. For this purpose, we consider energy-momentum prescription derived from the integral form of the constraint equations developed in the Hamiltonian formulation of the teleparallel equivalent of General Relativity. We use this technique to investigate energy-momentum of stationary axisymmetric Einstein-Maxwell solutions and cosmic string spacetimes. The angular momentum, gravitational and matter energy-momentum fluxes of these spacetimes are also evaluated. It is concluded that the results of teleparallel theory are relatively analogous to the results of General Relativity.
Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity
Canadian Journal of Physics, 2008
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
Energy-momentum distribution in General Relativity and teleparallel theory of gravitation
2008
Using the Møller and Landau-Lifshitz energy-momentum definitions in general relativity, we evaluate the energy-momentum distribution of the phantom black hole space-time. The phantom black hole model was applied to the supermassive black hole at the Galactic Centre. In both the aforementioned pseudotensorial prescriptions, the energy distribution depends on the mass M of the black hole, the phantom constant p and the radial coordinate r. Further, all the calculated momenta are found to be zero. The limiting cases r ! 0, r ! 1 and r ! À1 have also been the subject of the study.
Energy Momentum of Marder Universe in Teleparallel Gravity
International Journal of Theoretical Physics, 2007
In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of cylindrically-symmetric Marder universe, we consider the Møller, Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum definitions in the teleparallel gravity (TG). The energy-momentum distributions are found to be zero. These results are the same as a previous works of Aygün et al., they investigated the same problem in general relativity (GR) by using the Einstein, Møller, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Qadir–Sharif and Weinberg’s definitions. These results support the viewpoints of Banerjee–Sen, Xulu, Radinschi and Aydoğdu–Saltı. Another point is that our study agree with previous works of Cooperstock–Israelit, Rosen, Johri et al. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in teleparallel gravity. It is also independent of the 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.
The Nature of Gravitational Field and its Legitimate Energy–Momentum Tensor
Reports on Mathematical Physics, 2012
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity spacetimes) or that we even can dispense all those geometrical structures and simply represent the gravitational field as a field, in the Faraday's sense, living in Minkowski spacetime. The explicit Lagrangian density for this theory is given and the field equations (which are a set of four Maxwell's like equations) are shown to be equivalent to Einstein's equations. We also analyze if the teleparallel formulation can give a mathematical meaning to "Einstein's most happy thought", i.e. the equivalence principle. Moreover we discuss the Hamiltonian formalism for for our theory and its relation to one of the possible concepts for energy of the gravitational field which emerges from it and the concept of ADM energy. One of the main results of the paper is the identification in our theory of a legitimate energy-momentum tensor for the gravitational field expressible through a really nice formula. * This article is based on a talk given by the author at the 9 th International Conference on Cliffor Algebras and their Applications (ICCA9) Weimar, 15-20 July 2011.
Energy contents of some well-known solutions in teleparallel gravity
Astrophysics and Space Science, 2011
In the context of teleparallel equivalent to General Relativity, we study energy and its relevant quantities for some well-known black hole solutions. For this purpose, we use the Hamiltonian approach which gives reasonable and interesting results. We find that our results of energy exactly coincide with several prescriptions in General Relativity. This supports the claim that different energy-momentum prescriptions can give identical results for a given spacetime. We also evaluate energy-momentum flux of these solutions.
Energy Momentum Localization for Bianchi I-III-V-VI0 Universe in Teleparallel Gravity
2006
In this paper, considering the tele-parallel gravity versions of the Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum prescriptions energy and momentum distribution of the universe based on the general Bianchi type I-III-V-V I 0 universe and its transforms type I, III, V, V I 0 metrics, respectively which includes both the matter and gravitational fields are found. We obtain that Einstein and Bergmann-Thomson definitions of the energy-momentum complexes give the same results, while Landau-Lifshitz's energy-momentum definition does not provide same results for these type of metrics. This results are the same as a previous works of Aygün et al., the Authors investigate the same problem in general relativity by using the Einstein, Møller, Bergmann-Thomson, Landau-Lifshitz (LL) and Papapetrou's definitions. Furthermore, we show that for the Bianci type-I and type-V I 0 all the formulations give the same result. These results supports the viewpoints of Banerjee-Sen, Xulu and Aydoġdu-Saltı. Another point is that our study agree with previous works of Cooperstock-Israelit, Rosen, Johri et al., Radinschi and Aygün et al.. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in tele-parallel gravity.
Astrophysics and Space Science, 2008
In this paper, using the energy momentum definitions of the Einstein, Bergmann-Thomson, Landau-Lifshitz and Møller in general relativity (GR) and teleparallel gravity (TG), we have evaluated the energy-momentum distributions of Yilmaz-Rosen metric. We have obtained that these different energy-momentum definitions give different results in GR and TG. Furthermore these results are same in different gravitation theories and we get that both general relativity and teleparallel gravity are equivalent theories for Einstein, Bergmann-Thomson and Landau-Lifshitz prescriptions. Also, while the Møller energy definitions are same and zero but the momentum prescriptions are disagree in GR and TG.
The first order variation of the matter energy-momentum tensor Tµν with respect to the metric tensor g αβ plays an important role in modified gravity theories with geometry-matter coupling, and in particular in the f (R, T) modified gravity theory. We obtain the expression of the variation δTµν/δg αβ for the baryonic matter described by an equation given in a parametric form, with the basic thermodynamic variables represented by the particle number density, and by the specific entropy, respectively. The first variation of the matter energy-momentum tensor turns out to be independent on the matter Lagrangian, and can be expressed in terms of the pressure, the energymomentum tensor itself, and the matter fluid four-velocity. We apply the obtained results for the case of the f (R, T) gravity theory, where R is the Ricci scalar, and T is the trace of the matter energy-momentum tensor, which thus becomes a unique theory, also independent on the choice of the matter Lagrangian. A simple cosmological model, in which the Hilbert-Einstein Lagrangian is generalized through the addition of a term proportional to T n is considered in detail, and it is shown that it gives a very good description of the observational values of the Hubble parameter up to a redshift of z ≈ 2.5.