General Relativity and Gravitation

, Volume 45, Issue 2, pp 305–317 | Cite as

Instability of black hole formation under small pressure perturbations

Research Article

Abstract

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) (Oppenheimer and Snyder in Phys Rev 56:455, 1939; Datt in Zs f Phys 108:314, 1938). This extends a previous result on tangential pressures (Joshi and Malafarina Phys Rev D 83:024009, 2011) to the physically more realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.

Keywords

Gravitational collapse Black holes Naked singularity 

References

  1. 1.
    Oppenheimer, J.R., Snyder, H.: Phys. Rev. 56, 455 (1939)ADSMATHCrossRefGoogle Scholar
  2. 2.
    Datt, S.: Zs. f. Phys. 108, 314 (1938)ADSCrossRefGoogle Scholar
  3. 3.
    Joshi, P.S., Malafarina, D.: Phys. Rev. D 83, 024009 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    Penrose, R.: Riv. Nuovo Cimento 1, 252 (1969)Google Scholar
  5. 5.
    Joshi, P.S., Dwivedi, I.H.: Phys. Rev. D 47, 5357 (1993)ADSCrossRefGoogle Scholar
  6. 6.
    Waugh, B., Lake, K.: Phys. Rev. D 38, 1315 (1988)ADSCrossRefGoogle Scholar
  7. 7.
    Newman, R.P.A.C.: Class. Quantum Grav. 3, 527 (1986)ADSMATHCrossRefGoogle Scholar
  8. 8.
    Christodoulou, D.: Commun. Math. Phys. 93, 171 (1984)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Eardley, D.M., Smarr, L.: Phys. Rev. D 19, 2239 (1979)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Goncalves, S.M.C.V., Jhingan, S., Magli, G.: Phys. Rev. D 65, 064011 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    Magli, G.: Class. Quantum Grav. 14, 1937 (1997)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Magli, G.: Class. Quantum Grav. 15, 3215 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Harada, T., Nakao, K., Iguchi, H.: Class. Quantum Grav 16, 2785 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Joshi, P.S., Goswami, R.: Class. Quantum Grav. 19, 5229 (2002)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Joshi, P.S., Malafarina, D.: Int. J. Mod. Phys. D 20, 2641 (2011)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Ori, A., Piran, T.: Phys. Rev. Lett. 59, 2137 (1987)ADSCrossRefGoogle Scholar
  17. 17.
    Ori, A., Piran, T.: Gen. Relativ. Gravit. 20, 7 (1988)MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Ori, A., Piran, T.: Phys. Rev. D 42, 1068 (1990)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Joshi, P.S., Dwivedi, I.H.: Commun. Math. Phys. 146, 333 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    Joshi, P.S., Dwivedi, H.I.: Commun. Math. Phys. 166, 117 (1994)Google Scholar
  21. 21.
    Foglizzo, T., Henriksen, R.: Phys. Rev. D 48, 4645 (1993)ADSCrossRefGoogle Scholar
  22. 22.
    Harada, T.: Phys. Rev. D 58, 104015 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    Harada, T., Maeda, H.: Phys. Rev. D 63, 084022 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    Goswami, R., Joshi, P.S.: Class. Quantum Grav. 19, 5229 (2002)MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Giambó, R., Giannoni, F., Magli, G., Piccione, P.: Commun. Math. Phys. 235, 545 (2003)ADSMATHCrossRefGoogle Scholar
  26. 26.
    Giambo, R., Giannoni, F., Magli, G., Piccione, P.: Gen. Relativ. Gravit. 36, 1279 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Ghosh, S.G., Deshkar, D.W.: Int. J. Mod. Phys. D 12, 913 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  28. 28.
    Villas da Rocha, J.F., Wang, A.: Class. Quantum Grav. 17, 2589 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    Joshi, P.S., Krolak, A.: Class. Quantum Grav. 13, 3069 (1996)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    Gundlach, C.: ‘Critical phenomena’ on living reviews. http://relativity.livingreviews.org/Articles/lrr-2007-5
  31. 31.
    Garfinkle, D., Gundlach, C., Martn-Garca, J.M.: Phys. Rev. D 59, 104012 (1999)Google Scholar
  32. 32.
    Gundlach, C.: Phys. Rev. D 65, 064019 (2002)ADSCrossRefGoogle Scholar
  33. 33.
    Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., Pretorius, F.: Phys. Rev. D 68, 044007 (2003)MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    Choptuik, M.W., Hirschmann, E.W., Liebling, S.L., Pretorius, F.: Phys. Rev. Lett. 93, 131101 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    Sorkin, E.: Class. Quantum Grav. 28, 025011 (2011)MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    Oppenheimer, J.R., Volkoff, G.M.: Phys. Rev. 55, 374 (1939)ADSMATHCrossRefGoogle Scholar
  37. 37.
    Bombaci, I.: Astron. Astrophys. 305, 871 (1996)ADSGoogle Scholar
  38. 38.
    Woosley, S.E., Heger, A., Weaver, T.A.: Rev. Modern Phys. 74, 1015 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    Joshi, P.S.: Gravitational Collapse and Spacetime singularities. Cambridge University Press, Cambridge (2007)MATHCrossRefGoogle Scholar
  40. 40.
    Tolman, R.C.: Proc. Natl. Acad. Sci. USA 20, 410 (1934)Google Scholar
  41. 41.
    Bondi, H.: Mon. Not. Astron. Soc. 107, 343 (1947)MathSciNetGoogle Scholar
  42. 42.
    Lemaitre, G.: Ann. Soc. Sci. Bruxelles I 53, 51 (1933)Google Scholar
  43. 43.
    Joshi, P.S., Goswami, R.: Phys. Rev. D 76, 084026 (2007)MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    Joshi, P.S., Dwivedi, I.H.: Class. Quant. Grav. 16, 41 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  45. 45.
    Giambó, R.: Class. Quant. Grav. 22, 2295 (2005)ADSMATHCrossRefGoogle Scholar
  46. 46.
    Patil, M., Joshi, P.S.: Phys. Rev. D 82, 104049 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    Patil, M., Joshi, P.S., Malafarina, D.: Rev. D 83, 064007 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Tata Institute of Fundamental ResearchMumbaiIndia

Personalised recommendations