Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity

Abstract

The energy momentum localization problem is one of the old, very interesting and unsolved puzzels in gravitational theories. Recently this significant problem has been extended to f(R)-gravity which is one of the famous modified theories gravity. In the present work, we consider generalized form of the Landau-Liftshitz energy-momentum relation in order to calculate energy distribution associated with the Bianchi VI(A) type space-time. Results were discussed numerically and specified by using of some well-known f (R)-gravity models given in literature.

Keywords

• Bianchi-type VI(A) spacetime,energy localization

Kütle Çekimsel f(R) Kuramında Bianchi-Type VI(A) Evreni için Yerelleşmiş Enerji

Abstract

Enerji momentum yerelleşme problemi oldukça eski ilginç ve halen çözüm bekleyen kütle-çekim kuramları bulmacasıdır. Son zamanlarda bu problem değiştirilmiş kütle-çekim kuramlarına genişletilmiştir. Sunulan bu çalışmada Bianchi VI(A) tipi uzay-zaman modeline eşlik eden enerji dağılımını hesaplamak için genelleştirilmiş Landau-Liftshitz enerji tanımı göz önünde bulunduruldu. Sonrasında, sonuçlar nümerik olarak analiz edildi. Ek olarak, literatürde iyi bilinen bazı f(R)-gravite modelleri için elde edilen sonuçlar özel durumlara indirgendi.

Keywords

• Bianchi-tipi VI(A) uzay zaman,enerji yerelleşmesi

References

1. Amir, M.J., Naheed, S., 2013. Spatially homogeneous rotating solution in f (R) gravity and its energy contents. Int. J. Theor. Phys., 52:1688-1695.
2. Aydoğdu, O., Saltı, M., 2006. Energy density associated with the Bianchi type-II space-time. Prog. Theor. Phys., 98:115, 63-71.
3. Bergmann, P.G., Thompson, R., 1953. Spin and angular momentum in general relativity. Phys. Rev., 89:400-407.
4. Capozziello, S., 2002. Curvature quintessence. Int. J. Mod. Phys. D., 11:483-491.
5. Capozziello, S., De Laurentis, M., 2011. Extended theories of gravity. Phys. Rept., 509:167-324.
6. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S., 2004. Is cosmic speed-up due to new gravitational physics? Phys. Rev. D., 70:043528.
7. Einstein, A., 1915. Erklarung der Perihelionbewegung der Merkur aus der allgemeinen Relativitatstheorie. Preuss. Akad. Wiss. Berlin, 47:778-799.
8. Fagundes, H.V., 1992. Closed spaces in cosmology. Gen. Rel. Grav., 24:199-217.

9. Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y., 2007. Constraining f (R) gravity as a scalar-tensor theory. Phys. Rev.D, 76:063505.
10. Hendi, S.H., Eslam Panah, B., Corda, C., 2014. Asymptotically Lifshitz black hole solutions in F (R) gravity. Can. J. Phys., 92:76-81.
11. Landau, L.D., Liftshitz E.M., 1951. The Classical Theory of Fields. Addison-Wesley Press, Reading, MA.
12. Møller, C., 1958. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys.
13. (N.Y.), 4:347-371.
14. Multamäki, T., Putaja, A., Vagenas, E.C., Vilja I., 2008. Energy-momentum complexes in f (R) theories of gravity. Class. Quant. Grav., 25:075017.
15. Nojiri, S., Odintsov, S.D., 2004. Modified gravity with in R terms and cosmic acceleration. Gen. Rel. Grav., 36:1765-1780.
16. Nojiri, S., Odintsov S.D., 2007. Introduction to modified gravity and gravitational alternative for dark energy. Int. J. Geom. Meth. Mod. Phys., 4:115-146.
17. Papapetrou, A., 1948. Einstein’s theory of gravitation and flat space. Proc. R. Ir. Acad. A, 52:11-23.
18. Rosen, N., Virbhadra, K.S., 1993. Energy and momentum of cylindrical gravitational waves. Gen. Rel. Grav., 25:429-433.
19. Salti, M., Aydogdu, O., 2006. Energy in the Schwarzschild-de Sitter spacetime. Found. Phys. Lett., 19:269-276.
20. Salti M., Korunur M., Açıkgöz, I., 2013. Gödel-type spacetimes in f(R)-gravity. Cent. Eur. J. Phys., 11:961-967.
21. Sharif, M., Farasat, M., 2009. Exact solutions of Bianchi-type I and V spacetimes in the f(R) theory of gravity. Class. Quant. Grav., 26:235020.
22. Sharif, M., Farasat, M., 2010. Energy distribution in f (R) gravity. Gen. Rel. Grav., 42:1557-1569.
23. Starobinsky, A.A.A., 1980. New type of isotropic cosmological models without singularity. Phys. Lett. B, 91:99-102.
24. Starobinsky, A.A.A., 2007. Disappearing cosmological constant in f (R) gravity. JETP Lett., 86:157-163.
25. Tolman, R.C., 1934. Relativity, thermodynamics and cosmology. Oxford University Press, London.
26. Vagenas, E.C., 2003. Energy distribution in 2D stringy black hole backgrounds. Int. J. Mod. Phys. A, 18:5781-5794.
27. Virbhadra, K.S., 1990. Energy associated with a Kerr-Newman black hole. Phys. Rev. D, 41:1086-1090.
28. Weinberg, S., 1972. Gravitation and cosmlogy: Principles and applications of general theory of relativity. Wiley, New York.
29. Xulu, S.S., 2000. Møller energy for the Kerr-Newman metric. Mod. Phys. Lett. A, 15:1511-1517.