Abstract
We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of f(R) gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the collapsing fluid, Newtonian and post Newtonian regimes are taken into account. The field equations are investigated for a well-known f(R) model of the form R+δR 2 admitting Schwarzschild solution. The perturbation scheme is used on the dynamical equations to explore the instability conditions of expansionfree fluid evolution. We conclude that instability conditions depend upon pressure anisotropy, energy density and some constraints arising from this theory.
Similar content being viewed by others
References
Carroll, S.M., et al.: New J. Phys. 8, 323 (2006)
Carloni, S., Dunsby, P.K.S., Troisi, A.: Phys. Rev. D 77, 024024 (2008)
Chandrasekhar, S.: Astrophys. J. 140, 417 (1964)
Chiba, T.: Phys. Lett. B 575, 1 (2003)
Chan, R., et al.: Mon. Not. R. Astron. Soc. 239, 91 (1989)
Chan, R., Herrera, L., Santos, N.O.: Mon. Not. R. Astron. Soc. 265, 533 (1993)
Chan, R., Herrera, L., Santos, N.O.: Mon. Not. R. Astron. Soc. 267, 637 (1994)
Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)
de la Cruz-Dombriz, A., Dobado, A.: Phys. Rev. D 74, 087501 (2006)
de la Cruz-Dombriz, A., Dobado, A., Maroto, A.L.: Phys. Rev. D 80, 124011 (2009a)
de la Cruz-Dombriz, A., Dobado, A., Maroto, A.L.: In: Proceedings of Spanish Relativity Meeting, Spain (2009b)
Herrera, L., Santos, N.O.: Phys. Rev. D 70, 084004 (2004)
Herrera, L., Santos, N.O., Le Denmat, G.: Mon. Not. R. Astron. Soc. 237, 257 (1989)
Herrera, L., Santos, N.O., Wang, A.: Phys. Rev. D 78, 080426 (2008)
Herrera, L., Santos, N.O., Le Denmat, G.: Dynamical instability of expansion-free fluids. arXiv:1010.1518 (2010)
Hwang, J.C., Noh, H.: Phys. Rev. D 54, 1460 (2006)
Joshi, P., Dadhich, N., Maartens, R.: Phys. Rev. D 65, 101501 (2002)
Liddle, A.R., Wands, D.: Mon. Not. R. Astron. Soc. 253, 637 (1991)
Misner, C.W., Sharp, D.: Phys. Rev. 136, B571 (1964)
Mignemi, S., Wiltshire, D.L.: Phys. Rev. D 46, 1475 (1992)
Rudnick, L., Brown, S., Williams, L.R.: Astrophys. J. 671, 40 (2007)
Sharif, M., Kausar, H.R.: Mod. Phys. Lett. A 25, 3299 (2010)
Sharif, M., Kausar, H.R.: Int. J. Mod. Phys. D (2011a, to appear)
Sharif, M., Kausar, H.R.: Astrophys. Space Sci. 331, 281 (2011b)
Sharif, M., Kausar, H.R.: Astrophys. Space Sci. 332, 463 (2011c)
Sharif, M., Kausar, H.R.: J. Phys. Soc. Jpn. 80, 044004 (2011d)
Sharif, M., Kausar, H.R.: Phys. Lett. B 697, 01 (2011e)
Sharif, M., Kausar, H.R.: J. Cosmol. Astropart. Phys. 7, 022 (2011f)
Skripkin, V.A.: Sov. Phys. Dokl. 135, 1183 (1960)
Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)
Tikhonov, A.V., Karachentsev, I.D.: Astrophys. J. 653, 969 (2006)
Tsujikawa, S., Uddin, K., Tavakol, R.: Phys. Rev. D 77, 043007 (2008)
Mazharimousavi, S.H., Halilsoy, M.: Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field. arXiv:1105.3659v3 (2011)
Moon, T., Myung, Y.S., Son, E.J.: f(R) black holes, Gen. Relativ. Gravit. (2011, to appear)
Whitt, B.: Phys. Lett. B 145, 176 (1984)
Wheeler, J.A., et al.: Gravitation and Gravitational Collapse. University of Chicago Press, Chicago (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sharif, M., Kausar, H.R. Newtonian and post Newtonian expansionfree fluid evolution in f(R) gravity. Astrophys Space Sci 337, 805–813 (2012). https://doi.org/10.1007/s10509-011-0863-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-011-0863-y