Abstract
In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f(R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f(R 0) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f(R 0) plays the role of the cosmological constant.
Similar content being viewed by others
References
Abdalla, M.C.B., Nojiri, S., Odintsov, S.D.: Class. Quantum Gravity 22, L35 (2005)
Amendola, L., Tsujikawa, S.: Phys. Lett. B 660, 125 (2008)
Amendola, L., Polarski, D., Tsujikawa, S.: Phys. Rev. Lett. 98, 131302 (2007)
Bergliaffa, S.E.P.: Phys. Lett. B 642, 311 (2006)
Bertolami, O., Pármos, J.: Class. Quantum Gravity 25, 245017 (2008)
Bertolami, O., Sequeira, M.C.: Phys. Rev. D 79, 104010 (2009)
Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002)
Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008)
Capozziello, S., Stabile, A., Troisi, A.: Class. Quantum Gravity 25, 085005 (2008)
Chiba, T.: Phys. Lett. B 575, 1 (2003)
Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)
Dev, A., et al.: Phys. Rev. D 78, 083515 (2008)
Dicke, R.: Gen. Relativ. Gravit. 36, 217 (2004)
Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)
Eardley, D.M., Smarr, L.: Phys. Rev. D 19, 2239 (1979)
Erickcek, A.L., Smith, T.L., Kamionkowski, M.: Phys. Rev. D 74, 121501 (2006)
Faraoni, V.: Phys. Rev. D 74, 104017 (2006)
Frolov, A.V.: Phys. Rev. Lett. 101, 061103 (2008)
Harada, T.: Phys. Rev. D 58, 104015 (1998)
Harko, T.: Phys. Lett. B 669, 376 (2008)
Hawking, S.W.: Proc. R. Soc. Lond. A 300, 187 (1967)
Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge (1975)
Hawking, S.W., Penrose, R.: Proc. R. Soc. Lond. A 314, 529 (1970)
Hayward, S.A., Shiromizu, T., Nakao, K.: Phys. Rev. D 49, 5080 (1994)
Herrera, L., Santos, N.O.: Phys. Rev. D 70, 084004 (2004)
Israel, W.: Nuovo Cimento B 44, 1 (1966)
Israel, W.: Nuovo Cimento B 48, 463 (1967) (E)
Joshi, P.S.: Global Aspects in Gravitation and Cosmology. Oxford University Press, Oxford (1993)
Joshi, P.S., Dwivedi, I.H.: Commun. Math. Phys. 166, 117 (1994)
Joshi, P.S., Dwivedi, I.H.: Class. Quantum Gravity 16, 41 (1999)
Kainulainen, K., Reijonen, V., Sunhede, D.: Phys. Rev. D 76, 043503 (2007)
Kung, J.H.: Phys. Rev. D 53, 3017 (1996)
Lake, K.: Phys. Rev. Lett. 68, 3129 (1992)
Lake, K.: Phys. Rev. D 62, 027301 (2000)
Lecian, O.M., Montani, G.: Class. Quantum Gravity 26, 045014 (2009)
Markovic, D., Shapiro, S.L.: Phys. Rev. D 61, 084029 (2000)
Misner, C.W., Sharp, D.: Phys. Rev. 136, b571 (1964)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 646, 105 (2007)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 659, 821 (2008)
Oppenheimer, J.R., Synder, H.: Phys. Rev. 56, 455 (1939)
Ori, A., Piran, T.: Phys. Rev. Lett. 59, 2137 (1987)
Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003)
Penrose, R.: Phys. Rev. Lett. 14, 57 (1965)
Penrose, R.: Riv. Nuovo Cimento 1, 252 (1969)
Sahani, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 9, 373 (2000)
Sahani, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 15, 2195 (2006)
Sami, M.: Lect. Notes Phys. 72, 219 (2007)
Santose, J., Alcaniz, J.S., Carvalho, F.C., Pires, N.: Phys. Lett. B 669, 14 (2008)
Sharif, M., Abbas, G.: Mod. Phys. Lett. A 24, 2551 (2009)
Sharif, M., Ahmad, Z.: Mod. Phys. Lett. A 22, 2947 (2007a)
Sharif, M., Ahmad, Z.: Mod. Phys. Lett. A 22, 1493 (2007b)
Sharif, M., Ahmad, Z.: J. Korean Phys. Soc. 52, 980 (2008a)
Sharif, M., Ahmad, Z.: Acta Phys. Pol. B 39, 1337 (2008b)
Sotiriou, T.P.: Gen. Relativ. Gravit. 38, 1407 (2006a)
Sotiriou, T.P.: Phys. Rev. D 73, 063515 (2006b)
Sotiriou, T.P.: Class. Quantum Gravity 23, 5117 (2006c)
Sotiriou, T.P.: Phys. Lett. B 645, 389 (2007)
Szekers, P.: Commun. Math. Phys. 41, 55 (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sharif, M., Rizwana Kausar, H. Gravitational perfect fluid collapse in f(R) gravity. Astrophys Space Sci 331, 281–288 (2011). https://doi.org/10.1007/s10509-010-0426-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-010-0426-7