Energy-momentum puzzle in a bianchi-type ıı universe with f(T) gravity

Year 2020, Volume: 41 Issue: 1, 290 - 297, 22.03.2020

Murat Korunur

https://doi.org/10.17776/csj.514174

Cited By: 1

Abstract

The energy-momentum localization problem, which was attemted by Einstein himself for the first time, has been continued to the present day. Recently, new prescription obtained by modifying the torsion theory and these results shed light on the solution of the energy momentum localisation problem. Focusing this purpose, we consider a Locally Rotationally Symmetric Bianchi Type-II model in the teleparallel framework and calculate the modified energy and momentum density for the general case. We also obtain the energy and momentum density for some special cases of the modified theory and compare our results with previous work in the literature. 

Keywords

Energy-momentum localization, Bianch Type II universe, f(T) gravity

References

• [1] Einstein, Grundgedanken der allgemeinen Relativitätstheorie und Anwendung dieser Theorie in der Astronomie. A. Sitzungsber. Preus. Akad. Wiss. Berlin (Math. Phys.), 47 (1915) 778-786
• [2] Tolman R.C. Relativity, Thermodinamics and Cosmology. Oxford Univ. Pres. London, (1934).
• [3] Papapetrou A. Einstein’s theory of gravitation and flat space. Proc. R. Irish. Acad. A, 52 (1948) 11-23.
• [4] Bergmann P.G. and Thomson R. Spin and angular momentum in general relativity. Phys. Rev. 89 (1953) 400-407.
• [5] Møller C. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys. (NY), 4 (1958) 347-371.
• [6] Møller C. Further remarks on the localization of the energy in the general theory of relativity. Ann. Phys. (NY), 12 (1961) 118-133.
• [7] Weinberg S., Gravitation and Cosmology: Principle and Applications of General Theory of Relativity. John Wiley and Sons, Inc., New York, 1972.
• [8] Qadir A. and Sharif M., General Formula for the Momentum Imparted to Test Particles in Arbitrary Spacetimes. Physics Letters A, 167(4) (1992) 331-334.
• [9] Landau L.D. and Lifshitz E.M., The Classical Theory of Fields. Pergamon Press, 4th Edition, Oxford, 2002.
• [10] Mikhail F. I., Wanas M. I., Hindawi A. and Lashin E. I., Energy-momentum Complex in Møller's Tetrad Theory of Gravitation. International Journal of Theoretical Physics, 32(9) (1993) 1627-1642.
• [11] Virbhadra K. S., Energy Associated with a Kerr-Newman Black Hole. Physical Review D, 41(4) (1990) 1086.
• [12] Virbhadra K. S., Energy Distribution in Kerr-Newman Spacetime in Einstein’s as well as Møller’s Prescriptions. Physical Review D, 42(8) (1990) 2919.
• [13] Virbhadra K. S., Naked Singularities and Seifert’s Conjecture. Physical Review D, 60(10) (1999) 104041.
• [14] Cooperstock F.I. and Richardson S.A., In Proc. 4th Canadiand Conf. on General Relativity and Relativistic Astrophysics, World Scientific, Singapore, 1991.
• [15] Rosen N. and Virbhadra K. S., Energy and Momentum of Cylindrical Gravitational Waves. General Relativity and Gravitation, 25(4) (1993) 429-433.
• [16] Virbhadra K. S., Energy and Momentum of Cylindrical Gravitational Waves-II. Pramana J. Phys., 45(2) (1995) 215-219.
• [17] Chamorro A. And Virbhadra K. S., Energy Associated with Charged Dilaton Black Holes. International Journal of Modern Physics D, 5(03) (1996) 251-256.
• [18] Gad R. M., Energy and Momentum Associated with Solutions Exhibiting Directional Type Singularities. General Relativity and Gravitation, 38(3) (2006) 417-424.
• [19] Vagenas E. C., Energy Distribution in 2D Stringy Black Hole Backgrounds. International Journal of Modern Physics A, 18(31) (2003) 5781-5794.
• [20]. Vargas T., The Energy of the Universe in Teleparallel Gravity. General Relativity and Gravitation, 36(6) (2004) 1255-1264.
• [21] Salti M., Different Approaches for Møller's Energy in the Kasner-type Spacetime. Modern Physics Letters A, 20(28) (2005) 2175-2182.
• [22] Aydogdu O., Energy Distribution of the Universe in the Bianchi Type II Cosmological Models. Fortschritte der Physik: Progress of Physics, 54(4) (2006) 246-251.
• [23] Salti M. and Havare A., Energy–momentum in Viscous Kasner-Type Universe in Bergmann Thomson Formulations. International Journal of Modern Physics A, 20(10) (2005) 2169-2177.
• [24] Aydogdu O. and Salti M., Energy Density Associated with the Bianchi Type-II Space-Time. Progress of Theoretical Physics, 115(1) (2006) 63-71.
• [25] Korunur M., Salti M., and Havare A., On the Relative Energy Associated with Space-Times of Diagonal Metrics. Pramana J. Phys., 68(5) (2007) 735-748.
• [26] Aygün S., Tarhan I., and Baysal H. Scalar field theory and energy-momentum problem of Yilmaz-Rosen metric in general relativity and teleparallel gravity. Astrophysics and Space Science, 314(4) (2008) 323-330.
• [27] Kıy G. and Aygün S., Higher-dimensional energy–momentum problem for Bianchi types V and I universes in gravitation theories. International Journal of Geometric Methods in Modern Physics, 12(4) (2015) 1550045.
• [28] Özkurt Ş. and Aygün S., Energy distributions of Bianchi type-VIh Universe in general relativity and teleparallel gravity. Pramana J. Phys., 88- 66 (2017) 1-9.
• [29] Riess A. G., et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116(3) (1998) 1009.
• [30] Perlmutter S., et al., Measurements of Ω and Λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 517(2) (1999) 565.
• [31] Penzias A. A. and Wilson R. W., A Measurement of Excess Antenna Temperature at 4080 Mc/s. The Astrophysical Journal, 142 (1965) 419-421.
• [32] Lampeitl H., et al., First-Year Sloan Digital Sky Survey-II Supernova Results: Consistency and Constraints with Other İntermediate-Redshift Data Sets. Monthly Notices of the Royal Astronomical Society, 401(4) (2010) 2331-2342.
• [33] Adelman-McCarthy J. K., et al., The Sixth Data Release of the Sloan Digital Sky Survey. The Astrophysical Journal Supplement Series, 175(2) (2008) 297.
• [34] Boehmer C. G., Harko T. and Lobo F. S., Wormhole Geometries in Modified Teleparallel Gravity and the Energy Conditions. Physical Review D, 85(4) (2012) 044033.
• [35] Setare M. R. and Mohammadipour N., Cosmological Viability Conditions for f (T) Dark Energy Models. Journal of Cosmology and Astroparticle Physics, 2012(11) (2012) 030.
• [36] Myrzakulov R., F (T) Gravity and k-essence. General Relativity and Gravitation, 44(12) (2012) 3059-3080.
• [37] Aldrovandi R. and Pereira J. G., An Introduction to Geometrical Physics, Singapore, World Scientific, 1995.
• [38] Abedi H. and Salti M., Multiple Field Modified Gravity and Localized Energy in Teleparallel Framework. General Relativity and Gravitation, 47(8) (2015) 93.
• [39] Lorenz D., An Exact Bianchi-Type II Cosmological Model with Matter and an Electromagnetic Field. Physics Letters A, 79(1) (1980) 19-20.
• [40] Nunes R. C., Pan S., Nunes R.C., Pan S., and Saridakis E.N., New Observational Constraints on f(T) Gravity from Cosmic Chronometers. J. Cosmol. Astropart. Phys., 08 (2016) 011.
• [41] Myrzakulov R., Cosmology of F(T) Gravity and k-Essence. Entropy, 14(9) (2012) 1627-1651.
• [42] Karami K. and Abdolmaleki A., Generalized Second Law of Thermodynamics in f (T) Gravity. Journal of Cosmology and Astroparticle Physics, 2012(04) (2012) 007.
• [43] Sahoo P. K., et al., Einstein Energy-momentum Complex for a Phantom Black Hole Metric. Chinese Physics Letters, 32(2) (2015) 020402.
• [44] Grace S. A., New Developments in String Theory Research. Nova Publishers, 2006.