ENERGY–MOMENTUM DISTRIBUTIONS OF FIVE-DIMENSIONAL HOMOGENEOUS-ANISOTROPIC UNIVERSES

2012 ◽  
Vol 21 (10) ◽  
pp. 1250078 ◽  
Author(s):  
MELİS ULU DOGRU ◽  
DERYA BAYKAL ◽  
GÜLİZ KIY ◽  
DOGUKAN TASER ◽  
HALİFE CAGLAR ◽  
...  
Keyword(s):  
General Relativity ◽  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Type I ◽  
Bianchi Type I ◽  
Type Iii ◽  
Momentum Distributions ◽  
Energy And Momentum ◽  
Type V

In this study, it has been investigated whether the energy and momentum can be localizable for five-dimensional homogeneous and anisotropic universes. In this connection, energy and momentum of five-dimensional Bianchi type-I, type-III and type-V spacetimes have been calculated in the framework of general relativity (GR) and teleparallel gravity (TG). Einstein, Bergmann–Thomson, Landau–Lifshitz, Papapetrou, Tolman and Møller energy–momentum complexes have been used to obtain these related quantities of given the spacetimes in GR, while Einstein, Bergmann–Thomson, Landau–Lifshitz and Møller prescriptions have been used to obtain these related quantities of the spacetimes in TG. It has been found that all of the energy and momentum distributions of five-dimensional Bianchi type-I spacetime are equal to zero in GR and TG. For five-dimensional Bianchi type-III and type-V spacetimes, Bergmann–Thomson, Einstein and Tolman energy and momentum components give the same results, however Møller, Landau–Lifshitz and Papapetrou energy–momentum distributions give different results in general relativity. Also, in TG, Bergmann–Thomson and Einstein energy and momentum components give the same results for the Bianchi type-III and type-V spacetimes, too. In this sense, it is seen that Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum descriptions of these spacetimes have been given same results in both theories, GR and TG.

Energy–momentum distributions of Ruban universe in general relativity and teleparallel gravity

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950011 ◽  
Author(s):  
C. Aktaş
Keyword(s):  
General Relativity ◽  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Type I ◽  
Universe Model ◽  
Zero Energy ◽  
Bianchi Type I ◽  
Momentum Distributions ◽  
Bianchi Type I Universe

In this study, we obtain Einstein, Bergmann–Thomson (BT), Landau–Lifshitz (LL), Møller, Papapetrou (PP) and Tolman energy–momentum (EM) distributions for Ruban universe model in general relativity (GR) and teleparallel gravity (TG). We obtain same results for Einstein, Bergmann–Thomson and Landau–Lifshitz energy–momentum distributions in GR and TG. Also, we get same results for Einstein and Tolman energy–momentum distributions in GR. The Møller energy–momentum results are different in GR and TG. Also, using Ruban universe model, we obtain LRS Bianchi type I solutions and we get zero energy–momentum results for this universe model in GR and TG. These results of LRS Bianchi type I universe model agree with Aygün et al., Taşer et al., Doğru et al., Banerjee–Sen, Tryon and Xulu in different gravitation theories.

Higher-dimensional energy–momentum problem for Bianchi types V and I universes in gravitation theories

2015 ◽  
Vol 12 (04) ◽  
pp. 1550045 ◽  
Author(s):  
Güliz Kiy ◽  
Sezgin Aygün
Keyword(s):  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Type I ◽  
Four Dimensions ◽  
Momentum Distributions ◽  
Energy And Momentum ◽  
Bianchi Type V Universe ◽  
Energy And Momentum Densities ◽  
Type V ◽  
Bianchi Type V

Using the Einstein, Bergmann–Thomson, Landau–Lifshitz, Møller, Papapetrou and Tolman energy–momentum complexes in general relativity (GR) and teleparallel gravity (TG), we calculate the total energy–momentum distributions associated with N-dimensional Bianchi type V universe. While the solutions of Einstein, Bergmann–Thomson and Tolman energy and momentum densities are the same as each other, the solutions of Landau–Lifshitz, Møller and Papapetrou energy–momentum densities are different for N-dimensional Bianchi type V space-time in GR and TG. Obtained results for Einstein, Bergmann–Thomson and Landau–Lifshitz definitions we could say that GR and TG are in the same class. Because different energy–momentum distributions provide same results. However we have discussed N-dimensional Bianchi type I solutions and then we obtained all energy–momentum solutions are vanish in GR and TG theories. These results agree with Banerjee–Sen, Xulu, Aydoḡdu–Saltı and Radinschi in four dimensions.

scholarly journals ENERGY-MOMENTUM LOCALIZATION PROBLEM IN HIGHER DIMENSIONAL KASNER TYPE UNIVERSE MODEL

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Sezgin AYGÜN
Keyword(s):  
Bianchi Type ◽  
Relativity Theory ◽  
Type I ◽  
Universe Model ◽  
Frw Universe ◽  
Bianchi Type I ◽  
Higher Dimensional ◽  
Momentum Distributions ◽  
Bianchi Type I Universe ◽  
Energy And Momentum

Considering Landau-Lifshitz (LL), Papapetrou (PP), Bergmann-Thomson (BT), Møller (ML), Einstein (EI) and Tolman (TL) energy and momentum prescriptions in general relativity theory (GR) and the tetrad theory of gravity (TG), we get total energy and momentum distributions based on  dimensional Kasner type universe model. Using different energy and momentum prescriptions, we obtain zero energy and momentum distributions in different gravitation theories. Also, we calculate two and three dimensional Kasner type universe solutions in GR and TG. Our solutions consist with each other. The obtained results are agree with previous studies of Kıy and Aygün for higher dimensional Bianchi type I universe, Do ru et al. for 5-D Bianchi type I universe, Banerjee, Xulu, Aydo du and Saltı, Radinschi, Lau and Vargas for 4-D Bianchi type I universe, Taşer et al. for 5-D Kasner universe, Havare and Saltı, Saltı for 4-D Kasner solutions, Tryon, Cooperstock, Rosen and Johri et al. for 4-D FRW universe in GR and TG.  All these studies, the authors have obtained the energy-momentum distribution is zero in GR and TG. However we could say that GR and TG are equivalent and these definitions are working properly for higher dimensional Kasner type universe in GR and TG.

Homothetic vector field in plane symmetric Bianchi type-I cosmological model in Lyra geometry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450116 ◽  
Author(s):  
Ragab M. Gad ◽  
A. S. Alofi
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Riemannian Geometry ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type I ◽  
Bianchi Type I ◽  
Plane Symmetric ◽  
Homothetic Vector

In this paper, we obtain a homothetic vector field of a plane symmetric Bianchi type-I spacetime based on Lyra geometry. We discuss the cases when the displacement vector is function of t and when it is constant. We investigate the equation of state in both two cases. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity (GR), based on Riemannian geometry, will be given.

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.

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