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

Year 2016, Volume: 2 Issue: 2, 64 - 69, 28.12.2016

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.

References

  • 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.
  • Aydoğdu, O., Saltı, M., 2006. Energy density associated with the Bianchi type-II space-time. Prog. Theor. Phys., 98:115, 63-71.
  • Bergmann, P.G., Thompson, R., 1953. Spin and angular momentum in general relativity. Phys. Rev., 89:400-407.
  • Capozziello, S., 2002. Curvature quintessence. Int. J. Mod. Phys. D., 11:483-491.
  • Capozziello, S., De Laurentis, M., 2011. Extended theories of gravity. Phys. Rept., 509:167-324.
  • 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.
  • Einstein, A., 1915. Erklarung der Perihelionbewegung der Merkur aus der allgemeinen Relativitatstheorie. Preuss. Akad. Wiss. Berlin, 47:778-799.
  • Fagundes, H.V., 1992. Closed spaces in cosmology. Gen. Rel. Grav., 24:199-217.
  • Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y., 2007. Constraining f (R) gravity as a scalar-tensor theory. Phys. Rev.D, 76:063505.
  • Hendi, S.H., Eslam Panah, B., Corda, C., 2014. Asymptotically Lifshitz black hole solutions in F (R) gravity. Can. J. Phys., 92:76-81.
  • Landau, L.D., Liftshitz E.M., 1951. The Classical Theory of Fields. Addison-Wesley Press, Reading, MA.
  • Møller, C., 1958. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys.
  • (N.Y.), 4:347-371.
  • Multamäki, T., Putaja, A., Vagenas, E.C., Vilja I., 2008. Energy-momentum complexes in f (R) theories of gravity. Class. Quant. Grav., 25:075017.
  • Nojiri, S., Odintsov, S.D., 2004. Modified gravity with in R terms and cosmic acceleration. Gen. Rel. Grav., 36:1765-1780.
  • 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.
  • Papapetrou, A., 1948. Einstein’s theory of gravitation and flat space. Proc. R. Ir. Acad. A, 52:11-23.
  • Rosen, N., Virbhadra, K.S., 1993. Energy and momentum of cylindrical gravitational waves. Gen. Rel. Grav., 25:429-433.
  • Salti, M., Aydogdu, O., 2006. Energy in the Schwarzschild-de Sitter spacetime. Found. Phys. Lett., 19:269-276.
  • Salti M., Korunur M., Açıkgöz, I., 2013. Gödel-type spacetimes in f(R)-gravity. Cent. Eur. J. Phys., 11:961-967.
  • 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.
  • Sharif, M., Farasat, M., 2010. Energy distribution in f (R) gravity. Gen. Rel. Grav., 42:1557-1569.
  • Starobinsky, A.A.A., 1980. New type of isotropic cosmological models without singularity. Phys. Lett. B, 91:99-102.
  • Starobinsky, A.A.A., 2007. Disappearing cosmological constant in f (R) gravity. JETP Lett., 86:157-163.
  • Tolman, R.C., 1934. Relativity, thermodynamics and cosmology. Oxford University Press, London.
  • Vagenas, E.C., 2003. Energy distribution in 2D stringy black hole backgrounds. Int. J. Mod. Phys. A, 18:5781-5794.
  • Virbhadra, K.S., 1990. Energy associated with a Kerr-Newman black hole. Phys. Rev. D, 41:1086-1090.
  • Weinberg, S., 1972. Gravitation and cosmlogy: Principles and applications of general theory of relativity. Wiley, New York.
  • Xulu, S.S., 2000. Møller energy for the Kerr-Newman metric. Mod. Phys. Lett. A, 15:1511-1517.

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

Year 2016, Volume: 2 Issue: 2, 64 - 69, 28.12.2016

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.

References

  • 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.
  • Aydoğdu, O., Saltı, M., 2006. Energy density associated with the Bianchi type-II space-time. Prog. Theor. Phys., 98:115, 63-71.
  • Bergmann, P.G., Thompson, R., 1953. Spin and angular momentum in general relativity. Phys. Rev., 89:400-407.
  • Capozziello, S., 2002. Curvature quintessence. Int. J. Mod. Phys. D., 11:483-491.
  • Capozziello, S., De Laurentis, M., 2011. Extended theories of gravity. Phys. Rept., 509:167-324.
  • 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.
  • Einstein, A., 1915. Erklarung der Perihelionbewegung der Merkur aus der allgemeinen Relativitatstheorie. Preuss. Akad. Wiss. Berlin, 47:778-799.
  • Fagundes, H.V., 1992. Closed spaces in cosmology. Gen. Rel. Grav., 24:199-217.
  • Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y., 2007. Constraining f (R) gravity as a scalar-tensor theory. Phys. Rev.D, 76:063505.
  • Hendi, S.H., Eslam Panah, B., Corda, C., 2014. Asymptotically Lifshitz black hole solutions in F (R) gravity. Can. J. Phys., 92:76-81.
  • Landau, L.D., Liftshitz E.M., 1951. The Classical Theory of Fields. Addison-Wesley Press, Reading, MA.
  • Møller, C., 1958. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys.
  • (N.Y.), 4:347-371.
  • Multamäki, T., Putaja, A., Vagenas, E.C., Vilja I., 2008. Energy-momentum complexes in f (R) theories of gravity. Class. Quant. Grav., 25:075017.
  • Nojiri, S., Odintsov, S.D., 2004. Modified gravity with in R terms and cosmic acceleration. Gen. Rel. Grav., 36:1765-1780.
  • 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.
  • Papapetrou, A., 1948. Einstein’s theory of gravitation and flat space. Proc. R. Ir. Acad. A, 52:11-23.
  • Rosen, N., Virbhadra, K.S., 1993. Energy and momentum of cylindrical gravitational waves. Gen. Rel. Grav., 25:429-433.
  • Salti, M., Aydogdu, O., 2006. Energy in the Schwarzschild-de Sitter spacetime. Found. Phys. Lett., 19:269-276.
  • Salti M., Korunur M., Açıkgöz, I., 2013. Gödel-type spacetimes in f(R)-gravity. Cent. Eur. J. Phys., 11:961-967.
  • 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.
  • Sharif, M., Farasat, M., 2010. Energy distribution in f (R) gravity. Gen. Rel. Grav., 42:1557-1569.
  • Starobinsky, A.A.A., 1980. New type of isotropic cosmological models without singularity. Phys. Lett. B, 91:99-102.
  • Starobinsky, A.A.A., 2007. Disappearing cosmological constant in f (R) gravity. JETP Lett., 86:157-163.
  • Tolman, R.C., 1934. Relativity, thermodynamics and cosmology. Oxford University Press, London.
  • Vagenas, E.C., 2003. Energy distribution in 2D stringy black hole backgrounds. Int. J. Mod. Phys. A, 18:5781-5794.
  • Virbhadra, K.S., 1990. Energy associated with a Kerr-Newman black hole. Phys. Rev. D, 41:1086-1090.
  • Weinberg, S., 1972. Gravitation and cosmlogy: Principles and applications of general theory of relativity. Wiley, New York.
  • Xulu, S.S., 2000. Møller energy for the Kerr-Newman metric. Mod. Phys. Lett. A, 15:1511-1517.
There are 29 citations in total.

Details

Journal Section Articles
Authors

Murat Korunur

Publication Date December 28, 2016
Submission Date December 30, 2016
Published in Issue Year 2016 Volume: 2 Issue: 2

Cite

APA Korunur, M. (2016). Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity. International Journal of Pure and Applied Sciences, 2(2), 64-69.
AMA Korunur M. Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity. International Journal of Pure and Applied Sciences. December 2016;2(2):64-69.
Chicago Korunur, Murat. “Localized Energy Associated With Bianchi-Type VI(A) Universe in f(R) Theory of Gravity”. International Journal of Pure and Applied Sciences 2, no. 2 (December 2016): 64-69.
EndNote Korunur M (December 1, 2016) Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity. International Journal of Pure and Applied Sciences 2 2 64–69.
IEEE M. Korunur, “Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity”, International Journal of Pure and Applied Sciences, vol. 2, no. 2, pp. 64–69, 2016.
ISNAD Korunur, Murat. “Localized Energy Associated With Bianchi-Type VI(A) Universe in f(R) Theory of Gravity”. International Journal of Pure and Applied Sciences 2/2 (December 2016), 64-69.
JAMA Korunur M. Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity. International Journal of Pure and Applied Sciences. 2016;2:64–69.
MLA Korunur, Murat. “Localized Energy Associated With Bianchi-Type VI(A) Universe in f(R) Theory of Gravity”. International Journal of Pure and Applied Sciences, vol. 2, no. 2, 2016, pp. 64-69.
Vancouver Korunur M. Localized Energy Associated with Bianchi-Type VI(A) Universe in f(R) Theory of Gravity. International Journal of Pure and Applied Sciences. 2016;2(2):64-9.

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