Abstract
We study the gravitational collapse of a star with barotropic equation of state p = wρ in the context of \({f({\mathcal R})}\) theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as \({f({\mathcal R})=\alpha{\mathcal R}^{m}}\) , we show that for an appropriate initial value of the energy density, if α and m satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter α obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.
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Reynaud, S., Jaekel, M.-T.: (arXiv:gr-qc/0801.3407)
Hawking S.W., Ellis G.F.R.: The Large Scale Structure Of Spacetime. Cambridge University Press, Cambridge (1973)
Penrose R.: Phys. Rev. Lett. 14, 57 (1965)
Hawking S.W.: Proc. R. Soc. Lond. A 300, 187 (1967)
Hawking S.W., Penrose R.: Proc. R. Soc. Lond. A 314, 529 (1970)
Penrose R.: Riv Nuova Cimento 1 252 (1969). In: Hawking, S.W., Israel, W. (eds) General Relativity-An Einstein Centenary Survey, pp. 581–638. Cambridge University Press, Cambridge (1979)
Shapiro S.L., Teukolsky S.A.: Phys. Rev. Lett. 66, 994 (1991)
Shapiro S.L., Teukolsky S.A.: Phys. Rev. D 45, 2006 (1992)
Eardley D.M., Smarr L.: Phys. Rev. D 19, 2239 (1979)
Christodolou D.: Commun. Phys. (Lond.) 93, 171 (1984)
Joshi P.S., Singh T.P.: Phys. Rev. D 51, 6778 (1995)
Dwivedi I.H., Joshi P.S.: Class. Quantum Gravit. 14, 1223 (1997)
Saraykar R.V., Ghate S.H.: ibid 16, 281 (1989)
Ghate S.H., Saraykar R.V., Patil K.D., Patil K.D.: J. Phys. 53, 253 (1999)
Hiscok W.A., Williams L.G., Eardley D.M.: Phys. Rev. D 26, 751 (1982)
Kuroda Y.: Prog. Theor. Phys. 72, 63 (1984)
Rajagopal K., Lake K.: Phys. Rev. D 35, 1531 (1987)
Dwivedi I.H., Joshi P.S.: Class. Quantum Gravit. 6, 1599 (1989)
Joshi P.S., Dwivedi I.H.: Gen. Relativ. Gravit. 24, 129 (1992)
Lemos J.: Phys. Rev. Lett. 68, 1447 (1992)
Patil K.D., Saraykar R.V., Ghate S.H.: Pramana, J. Phys. 52, 553 (1999)
Ghosh S.G., Saraykar R.V.: Phys. Rev. D 62, 107502 (2000)
Ori A., Piran T.: Phys. Rev. D 42, 1068 (1990)
Joshi P.S., Dwivedi I.H.: Commun. Math. Phys. 146, 333 (1992)
Harada T.: Phys. Rev. D 58, 104015 (1998)
Szekeres P., Iyer V.: Phys. Rev. D 47, 4362 (1993)
Barve S., Singh T.P., Witten L.: Gen. Relativ. Gravit. 32, 697 (2000)
Mena F.C., Nolan B.C., Tavakol R.: Phys. Rev. D 70, 084030 (2004)
Gosh S.G., Dadhich N.: Gen. Relativ. Gravit. 35, 359 (2003)
Harko T., Cheng S.K.: Phys. Lett. A 226, 249 (2000)
Will C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge, UK (1981)
Schmidt H.-J.: Int. J. Geom. Meth. Phys. 4, 209 (2007)
Hehl F.W., Von Der Heyde P., Kerlick G.D., Nester J.M.: General relativity with spin and torsion: foundations and prospects. Rev. Mod. Phys. 48, 393 (1976)
Fujii Y., Maeda K.: The Scalar-Tensor Theory of Gravitation. Cambridge University Press, Cambridge, UK (2003)
Faraoni V.: Cosmology in Scalar-Tensor Gravity. Kluwer Academic, Dordrecht, Netherlands (2004)
Callan Jr.C.G., Coleman S., Jackiw R.: Ann. Phys. (NY) 59, 42 (1970)
Riess A.G. et al.: Astron. J. 116, 1009 (1998)
Perlmutter S. et al.: Nature 391, 51 (1998)
Riess A.G. et al.: Astron. J. 118, 2668 (1999)
Perlmutter S. et al.: Astrophys. J. 517, 565 (1999)
Riess A.G. et al.: Astrophys. J. 560, 49 (2001)
Tonry J.L. et al.: Astrophys. J. 594, 1 (2003)
Knop R. et al.: Astrophys. J. 598, 102 (2003)
Riess A.G. et al.: Astrophys. J. 607, 665 (2004)
Barris B. et al.: Astrophys. J. 602, 571 (2004)
De Felice A., Tsujikawa S.: Living Rev. Relativ. 13, 3 (2010)
Atazadeh K., Sepangi H.R.: Int. J. Mod. Phys. D 16, 687 (2007)
Carroll S.M., Duvvuri V., Trodden M., Turner M.S.: Phys. Rev. D 70, 043528 (2004)
Bean R., Bernat D., Pogosian L., Silvestri A., Trodden M.: Phys. Rev. D 75, 064020 (2007)
Atazadeh K., Farhoudi M., Sepangi H.R.: Phys. Lett. B 660, 275 (2008)
Nojiri S., Odintsov S.D.: Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007)
Nojiri S., Odintsov S.D.: Phys. Lett. B 576, 5 (2003)
Lovelock D.: J. Math. Phys. 12, 498 (1971)
Farhoudi M.: Gen. Relativ. Gravit. 38, 1261 (2006)
Farhoudi M.: Int. J. Mod. Phys. D 14, 1233 (2005)
Chiba T.: Phys. Lett. B 575, 1 (2003)
O’Hanlon J.: Phys. Rev. Lett. 29, 137 (1972)
Teyssandier P., Tourrenc P.: J. Math. Phys. 24, 2793 (1983)
Capozziello S.: Int. J. Mod. Phys. D 11, 483 (2002)
Capozziello S., Carloni S., Troisi A.: Recent Res. Dev. Astron. Astrophys. 1, 625 (2003)
Carloni S., Dunsby P.K.S., Capozziello S., Troisi A.: Class. Quantum Gravit. 22, 4839 (2005)
Sotiriou T.P., Faraoni V.: Rev. Mod. Phys. 82, 451 (2010)
Wands D.: Class. Quantum Gravit. 11, 269 (1994)
O’Hanlon J.: Phys. Rev. Lett. 29, 137 (1972)
Frolov, V.P., Novikov, I.D.: Black Hole Physics. Copenhagen & Edmonton (1997)
Malec E., Ó Murchadha N.: Phys. Rev. D 47, 1454 (1993)
Singh T.P.: Phys. Rev. D 58, 024004 (1998)
Kibble T.W.B.: J. Phys. A: Math. Gen. 9, 1387 (1976)
Weinberg S.: The Quantum Theory Of Fields, vol 2. Cambridge University Press, Cambridge (1995)
Arkani-Hamed N., Dimopoulos S., Dvali G.: Phys. Lett. B 429, 263 (1998)
Cohen M.I., Pfeiffer H.P., Scheel M.A.: Class. Quantum Gravit. 26, 035005 (2009)
Singh T.P., Joshi P.S.: Class. Quantum Gravit. 13, 559 (1996)
Garfinkle D., Comer Duncan G.: Phys. Rev. D 58, 064024 (1998)
Martín-García J.M., Gundlach C.: Phys. Rev. D 68, 024011 (2003)
Choptuik M.W.: Phys. Rev. Lett. 70, 9 (1993)
Abrahams A.M., Evans C.R.: Phys. Rev. Lett. 70, 2980 (1993)
Evans C.R., Coleman J.S.: Phys. Rev. Lett. 72, 1782 (1994)
Neilsen D.W., Choptuik M.W.: Class. Quantum Gravit. 17, 761 (2000)
Harada T., Harada T.: J. Phys. 63, 741 (2004)
Gundlach C., Martín-García J.M.: Living Rev. Relativ. 10, 5 (2007)
Vaidya P.C.: The external field of a radiating star in general relativity. Curr. Sci. 12, 183 (1943)
Vaidya P.C.: The gravitational field of a radiating star. Proc. Indian Acad. Sci. A. 33, 264 (1951)
Vaidya P.C.: Newtonian time in general relativity. Nature 171, 260 (1953)
Joshi, P.S.: Gravitational Collapse and Space-Time Singularities. Cambridge University Press, Cambridge (2007)
Harada T., Iguchi H., Nakao K.: Prog. Theor. Phys. 107, 449 (2002)
Gutti S., Singh T.P.: Phys. Rev. D 76, 064026 (2007)
Miyamoto U., Harada T.: Phys. Rev. D 69, 104005 (2004)
Hiscock W.A., Williams L.G., Eardley D.M.: Phys. Rev. D 26, 751 (1982)
Hiscock W.A.: Phys. Rev. D 23, 2813 (1981)
Ford L.H., Parker L.: Phys. Rev. D 17, 1485 (1978)
Vaz C., Witten L.: Phys. Lett. B 442, 90 (1998)
Joshi P.S., Dwivedi I.H.: Phys. Rev. D 47, 5357 (1993)
Waugh B., Lake K.: Phys. Rev. D 38, 1315 (1988)
Christodoulou D.: Ann. Math. 140, 607 (1994)
Faraoni V., Nadeau S.: Phys. Rev. D 72, 124005 (2005)
Capozziello S., De Laurentis M., Nojiri S., Odintsov S.D.: Phy. Rev. D 79, 124007 (2009)
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Ziaie, A.H., Atazadeh, K. & Rasouli, S.M.M. Naked singularity formation in \({f({\mathcal R})}\) gravity. Gen Relativ Gravit 43, 2943–2963 (2011). https://doi.org/10.1007/s10714-011-1216-4
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DOI: https://doi.org/10.1007/s10714-011-1216-4