Abstract
In this paper, we investigate static cylindrically symmetric solution in metric f(R) gravity by taking matter in the form of dust. The assumption of constant Ricci scalar curvature is taken to find the solution. The energy distribution of this solution is explored by applying Landau-Lifshitz energy-momentum complex. In addition, we explore the stability as well as constant scalar curvature conditions for some viable f(R) models along with their energy distribution. It is interesting to mention here that these models satisfy the above mentioned conditions.
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Astier, P., et al.: Astron. Astrophys. 447, 31 (2006)
Azadi, A., Momeni, D., Nouri-Zonoz, M.: Phys. Lett. B 670, 210 (2008)
Bean, R., et al.: Phys. Rev. D 75, 064020 (2007)
Bergmann, P.G., Thomson, R.: Phys. Rev. 89, 400 (1953)
Bolejko, K., et al.: Structures in the Universe by Exact Methods—Formation, Evolution, Interactions. Cambridge University Press, Cambridge (2009)
Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008)
Capozziello, S., Carloni, S., Troisi, A.: Recent Res. Dev. Astron. Astrophys. 1, 625 (2003)
Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005)
Capozziello, S., Stabile, A., Troisi, A.: Class. Quantum Gravity 24, 2153 (2007)
Caramês, T.R.P., de Mello, B.E.R.: Eur. Phys. J. C 64, 113 (2009)
Chiba, T.: Phys. Lett. B 575, 1 (2003)
Clifton, T., Barrow, J.D.: Phys. Rev. D 72, 103005 (2005)
Clifton, T., et al.: Phys. Rep. 513, 1 (2012)
De Felice, A., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010)
Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)
Eisenstein, D.J., et al.: Astrophys. J. 633, 560 (2005)
Faraoni, V., Nadeau, S.: Phys. Rev. D 72, 124005 (2005)
Flanagan, E.E.: Class. Quantum Gravity 21, 417 (2003)
Flanagan, E.E.: Class. Quantum Gravity 21, 3817 (2004)
Gödel, K.: Gen. Relativ. Gravit. 32, 1419 (2000)
Goldberg, J.N.: Phys. Rev. 111, 315 (1958)
Hollenstein, L., Lobo, F.S.N.: Phys. Rev. D 78, 124007 (2008)
Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007)
Kainulainen, K., Reijonen, V., Sunhede, D.: Phys. Rev. D 76, 043503 (2007)
Klepác, P.: J. Phys. Conf. Ser. 82, 012004 (2007)
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Addison-Wesley, Reading (1962)
Li, M., et al.: Commun. Theor. Phys. 56, 525 (2011)
Magnano, G., Sokolowski, L.M.: Phys. Rev. D 50, 5039 (1994)
Møller, C.: Ann. Phys. 4, 347 (1958)
Momeni, D., Gholizade, H.: Int. J. Mod. Phys. D 18, 1719 (2009)
Multamäki, T., Vilja, I.: Phys. Rev. D 74, 064022 (2006)
Multamäki, T., Vilja, I.: Phys. Rev. D 76, 064021 (2007)
Multamäki, T., et al.: Class. Quantum Gravity 25, 075017 (2008)
Noakes, D.R.: J. Math. Phys. 24, 1840 (1983)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)
Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 36, 176 (2004)
Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007a)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007b)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 77, 026007 (2008)
Papapetrou, A.: Proc. R. Ir. Acad. A 52, 11 (1948)
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Senovilla, J.M.M., Vera, R.: Class. Quantum Gravity 17, 2843 (2000)
Sharif, M.: Braz. J. Phys. 37, 1292 (2007)
Sharif, M., Amir, M.J.: Mod. Phys. Lett. A 22, 425 (2007a)
Sharif, M., Amir, M.J.: Gen. Relativ. Gravit. 39, 989 (2007b)
Sharif, M., Amir, M.J.: Mod. Phys. Lett. A 23, 3167 (2008a)
Sharif, M., Amir, M.J.: Int. J. Theor. Phys.. 47, 742 (2008b)
Sharif, M., Amir, M.J.: Can. J. Phys. 86, 1091 (2008c)
Sharif, M., Amir, M.J.: Can. J. Phys. 86, 1297 (2008d)
Sharif, M., Arif, S.: Mod. Phys. Lett. A (2012, to appear)
Sharif, M., Kausar, H.R.: J. Phys. Soc. Jpn. 80, 044004 (2011a)
Sharif, M., Kausar, H.R.: Astrophys. Space Sci. 332, 463 (2011b)
Sharif, M., Nazir, K.: Braz. J. Phys. 38, 156 (2008a)
Sharif, M., Nazir, K.: Commun. Theor. Phys. 50, 664 (2008b)
Sharif, M., Nazir, K.: Can. J. Phys. 86, 985 (2008c)
Sharif, M., Shamir, M.F.: Class. Quantum Gravity 26, 235020 (2009)
Sharif, M., Shamir, M.F.: Mod. Phys. Lett. A 25, 1281 (2010a)
Sharif, M., Shamir, M.F.: Gen. Relativ. Gravit. 42, 1557 (2010b)
Sharif, M., Taj, S.: Astrophys. Space Sci. 325, 75 (2010)
Shojai, A., Shojai, F.: Gen. Relativ. Gravit. 44, 211 (2012)
Song, Y.S., Hu, W., Sawicki, I.: Phys. Rev. D 75, 044004 (2007a)
Song, Y.S., Peiris, H., Hu, W.: Phys. Rev. D 76, 063517 (2007b)
Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)
Soussa, M.E., Woodard, R.P.: Gen. Relativ. Gravit. 36, 855 (2004)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 170, 377 (2007)
Starobinsky, A.A.: Phys. Lett. B 91, 99 (1980)
Starobinsky, A.A.: JETP Lett. 86, 157 (2007)
Tolman, R.C.: Relativity, Thermodynamics and Cosmology. Oxford University Press, London (1934)
Tsujikawa, S.: Phys. Rev. D 77, 023507 (2008)
Vilenkin, A., Shellard, E.P.S.: Cosmic Strings and Other Topological Defects. Cambridge University Press, Cambridge (1994)
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Sharif, M., Arif, S. Non-vacuum static cylindrically symmetric solution and energy distribution in f(R) gravity. Astrophys Space Sci 342, 237–243 (2012). https://doi.org/10.1007/s10509-012-1150-2
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DOI: https://doi.org/10.1007/s10509-012-1150-2