Advertisement

Gravitational Collapse of Fluid Bodies and Cosmic Censorship: Analytic Insights

  • S. Jhingan
  • G. Magli

Abstract

The present analytical understanding of the nature of the singularities which form at the end state of gravitational collapse of massive fluid bodies (“stars”) is reviewed. Special emphasis is given to the issue of the physical reasonableness of the models.

Keywords

Black Hole Perfect Fluid Gravitational Collapse Naked Singularity Trap Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hawking S.W., Ellis G.F.R. (1973): The Large Scale Structure of Space-Time. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  2. 2.
    Penrose R. (1969): Nuovo Cimento 1, 252Google Scholar
  3. 3.
    Joshi P.S. (1993): Global Aspects in Gravitation and Cosmology. Clarendon press, OxfordMATHGoogle Scholar
  4. 4.
    Rendall A.D. (1996): An introduction to the Einstein-Vlasov system (Lectures given at the Banach centre, Warsaw), gr-qc/9604001Google Scholar
  5. 5.
    Rein G., Rendall A.D., Schaeffer, J. (1998): Phys. Rev. D 58, 044007ADSCrossRefGoogle Scholar
  6. 6.
    Israel W. (1984): Found. Phys. 14, 1049MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Eardley D.M. (1987): Cosmic Strings and Origin of Structure in the Universe, in Gravitation and Astrophysics, Cargese Lectures, ed. by B. Carter, J. Hartle, Plenum, New York-London, pp. 293–305CrossRefGoogle Scholar
  8. 8.
    Clarke C.J.S. (1993): Class. Quantum Grav. 10, 1375Google Scholar
  9. 9.
    Wald R.M. (1998): Gravitational Collapse and Cosmic Censorship, in Black Holes, Gravitational Radiation and the Universe, Ess say s in the honour of C. V Vishveswara, ed. by R. Bala, B. Iyer and Biplab Bhawal, pp. 69–85Google Scholar
  10. 10.
    Joshi P.S. (1997): Gravitational Collapse, in Singularities, Black Holes and Cosmic Censorship, ed. by P.S. Joshi, IUCAA publication, Pune, India, pp. 33–54Google Scholar
  11. 11.
    Singh T.P. (1996): Gravitational Collapse and Cosmic Censorship, in Proc. of the XVIII th IAGRG meeting, ed. by G. Date, B. Iyer, Inst, of Math. Sci. Report 117, 57–76Google Scholar
  12. 12.
    Christodoulou D. (1994): Ann. Math. 140, 607MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Christodoulou D. (1999): Ann. Math. 149, 183MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Gundlach C. (1998): Adv. Theor. Math. Phys. 2, 1MathSciNetMATHGoogle Scholar
  15. 15.
    Burko L., Ori A. eds. (1998): The Internal Structure of Black Holes and Spacetime Singularities. Ann. Isr. Phys. Soc. 13 I.O.P., BristolGoogle Scholar
  16. 16.
    Thorne K.S. (1972): Nonspherical Gravitational Collapse: A Short Review, in Magic without Magic, ed. by J. R. Klauder, Freeman, San Francisco, pp. 231–258Google Scholar
  17. 17.
    Lemos J.P.S. (1999): Phys. Rev. D 59, 044020MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Israel W. (1986): Canad. J. Phys. 64, 120MathSciNetADSMATHCrossRefGoogle Scholar
  19. 19.
    Israel W. (1986): Phys. Rev. Lett. 56, 789MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Szekeres P. (1975): Phys. Rev. D 12, 2941ADSCrossRefGoogle Scholar
  21. 21.
    Joshi P.S., Krölak A. (1996): Class. Quantum Grav. 13, 3069ADSMATHCrossRefGoogle Scholar
  22. 22.
    Deshingkar S.S., Jhingan S., Joshi P.S. (1997): Gen. Rel. Grav. 27, 1071Google Scholar
  23. 23.
    Misner C.W., Sharp D.H. (1964): Phys. Rev. B 136, 571MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Magli G. (1997): Class. Quantum Grav. 14, 1937MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Herrera L., Martinez J. (1998): Gen. Rel. Grav. 30, 445MathSciNetADSMATHCrossRefGoogle Scholar
  26. 26.
    Kijowski J., Magli G. (1998): Class. Quantum Grav. 15, 3891MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Herrera L., Santos N. (1997): Phys. Rep. 286, 2MathSciNetCrossRefGoogle Scholar
  28. 28.
    Magli G. (1998): Class. Quantum Grav. 15, 3215MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    Lemaitre G. (1933): Ann. Soc. Sci. Bruxelles A 53, 51; (1997): Gen. Rel. Grav. 29, 641ADSGoogle Scholar
  30. 30.
    Joshi P.S., Dwivedi I.H. (1999): Class. Quantum Grav. 16, 41MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    Kramer D., Stephani H., Herlt E., MacCallum M. (1980): Exact Solutions of Einstein’s Field Equations. Cambridge University Press, CambridgeMATHGoogle Scholar
  32. 32.
    Krasinski A. (1997): Inhomogeneous Cosmological Models, Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  33. 33.
    Senovilla, J.M.M. (1998): Gen. Relativity Gravitation 30, 701MathSciNetADSMATHCrossRefGoogle Scholar
  34. 34.
    Bonnor W.B., Faulkes M.C. (1967): Mon. Not. Roy. Astr. Soc. 137, 239ADSGoogle Scholar
  35. 35.
    Thompson LH., Whitrow G.J. (1968): Mon. Not. Roy. Astr. Soc. 139, 499ADSMATHGoogle Scholar
  36. 36.
    Bondi H. (1969): Mon. Not. Roy. Astr. Soc. 142, 333ADSMATHGoogle Scholar
  37. 37.
    Mars M., Martm-Prats M., Senovilla J. (1996): Class. Quantum Grav. L 13, 51ADSCrossRefGoogle Scholar
  38. 38.
    Ayön-Beato E., Garcia A. (1998): Phys. Rev. Lett. 80, 5056ADSCrossRefGoogle Scholar
  39. 39.
    Magli G. (1999): Rep. Math. Phys. 44, 407–412MathSciNetADSMATHCrossRefGoogle Scholar
  40. 40.
    Hellaby C, Lake K. (1985): Ap. J. 290, 381ADSCrossRefGoogle Scholar
  41. 41.
    Newman R.P.A.C. (1986): Class. Quantum Grav. 3, 527ADSMATHCrossRefGoogle Scholar
  42. 42.
    Jhingan S., Joshi P.S. (1997): The Structure of Singularity in Spherical Inhomogeneous Dust Collapse, in The internal structure of black holes and spacetime singularities, ed. by L. Burko, A. Ori, Ann. Isr. Phys. Soc. 13, pp. 357–389Google Scholar
  43. 43.
    Yodzis P., Seifert H., Müller zum Hagen H. (1973): Comm. Math. Phys. 34, 135MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    Clarke C.J.S., Krölak A. (1986): J. Geom. and Phys. 2, 127ADSCrossRefGoogle Scholar
  45. 45.
    Clarke C.J.S. (1993): The Analysis of Space-Time Singularities, Cambridge University Press, CambridgeMATHGoogle Scholar
  46. 46.
    Clarke C.J.S., O’Donnell N. (1993): Ren. Sem. Mat. Un. Pol. Torino 50, 39MathSciNetGoogle Scholar
  47. 47.
    Papapetrou A., Hamoui A. (1967): Ann. Inst. Henri Poincaré 6, 343Google Scholar
  48. 48.
    Szekeres P., Lun A. (1997): What is a shell crossing singularity? Pre-printGoogle Scholar
  49. 49.
    Szekeres P., Iyer V. (1993): Phys. Rev. D 47, 4362MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    Dwivedi I.H., Joshi P.S. (1994): Comm. Math. Phys. 166, 117MathSciNetADSMATHCrossRefGoogle Scholar
  51. 51.
    Cooperstock F.I., Jhingan S., Joshi P.S., Singh, T.P. (1997): Class. Quantum Grav. 14, 2195MathSciNetADSMATHCrossRefGoogle Scholar
  52. 52.
    Eardley D.M. (1974): Phys. Rev. Lett. 33, 442ADSCrossRefGoogle Scholar
  53. 53.
    Eardley D.M., Smarr L. (1979): Phys. Rev. D 19, 2239MathSciNetADSCrossRefGoogle Scholar
  54. 54.
    Christodoulou D. (1984): Comm. Math. Phys. 93, 171MathSciNetADSCrossRefGoogle Scholar
  55. 55.
    Joshi P.S., Dwivedi I.H. (1993): Phys. Rev. D 47, 5357ADSCrossRefGoogle Scholar
  56. 56.
    Tolman R.C. (1934): Proc. Nat. Acad. Sci. 20, 169ADSCrossRefGoogle Scholar
  57. 57.
    Bondi H. (1947): Mon. Not. Roy. Astr. Soc. 107, 410MathSciNetADSMATHGoogle Scholar
  58. 58.
    Oppenheimer J., Snyder H. (1939): Phys. Rev. 56, 455ADSMATHCrossRefGoogle Scholar
  59. 59.
    Gorini V., Grillo G., Pelizza M. (1989): Phys. Lett. A 135, 154MathSciNetADSCrossRefGoogle Scholar
  60. 60.
    Grillo G. (1991): Class. Quantum Grav. 8, 739MathSciNetADSMATHCrossRefGoogle Scholar
  61. 61.
    Lake K. (1992): Phys. Rev. Lett. 68, 3129MathSciNetADSMATHCrossRefGoogle Scholar
  62. 62.
    Singh T.P., Joshi P.S. (1996): Class. Quantum Grav. 13, 559MathSciNetADSMATHCrossRefGoogle Scholar
  63. 63.
    Ori A. (1990): Class. Quantum Grav. 7, 985MathSciNetADSCrossRefGoogle Scholar
  64. 64.
    Singh T.P., Witten L. (1997): Class. Quantum Grav. 14, 3489MathSciNetADSMATHCrossRefGoogle Scholar
  65. 65.
    Barve S., Singh T.P., Witten L.: Spherical gravitational collapse: tangential pressure and related equations of state, gr-qc/9901080Google Scholar
  66. 66.
    Einstein A. (1939): Ann. Math. 40(4), 922CrossRefGoogle Scholar
  67. 67.
    Datta B. K. (1970): Gen. Rel. Grav. 1, 19ADSCrossRefGoogle Scholar
  68. 68.
    Bondi H. (1971): Gen. Rel. Grav. 2, 321MathSciNetADSCrossRefGoogle Scholar
  69. 69.
    Harada T., Iguchi H., Nakao K. (1998): Phys. Rev. D 58, R041502MathSciNetADSCrossRefGoogle Scholar
  70. 70.
    Jhingan S., Magli G.: Black holes vs. naked singularities formation in collapsing Einstein’s clusters, Phys. Rev. D, in pressGoogle Scholar
  71. 71.
    Carr B., Coley A.A.: A complete classification of spherically symmetric perfect fluid similarity solutions, Phys. Rev. D, in pressGoogle Scholar
  72. 72.
    Bogoyavlenski O.I. (1985): Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics. Springer, Berlin-Heidelberg-New YorkCrossRefGoogle Scholar
  73. 73.
    Carr B.J. (2000): Spherically symmetric similarity solutions, in Proc. 7 th Canadian Conference on General Relativity and Relativistic Astrophysics, ed. by D. Hobill, in pressGoogle Scholar
  74. 74.
    Waugh B., Lake K. (1988): Phys. Rev. D 38, 1315ADSCrossRefGoogle Scholar
  75. 75.
    Ori A., Piran T. (1990): Phys. Rev. D 42, 1068MathSciNetADSCrossRefGoogle Scholar
  76. 76.
    Lemos J.P.S. (1991): Phys. Lett. A 158, 279MathSciNetADSCrossRefGoogle Scholar
  77. 77.
    Lemos J.P.S. (1992): Phys. Rev. Lett. 68, 1447MathSciNetADSMATHCrossRefGoogle Scholar
  78. 78.
    Ori A., Piran T. (1987): Phys. Rev. Lett. 59, 2137ADSCrossRefGoogle Scholar
  79. 79.
    Joshi P.S., Dwivedi I.H. (1992): Comm. Math. Phys. 146, 333MathSciNetADSMATHCrossRefGoogle Scholar
  80. 80.
    Kuroda Y (1984): Prog. Theor. Phys. 72, 63MathSciNetADSMATHCrossRefGoogle Scholar
  81. 81.
    Papapetrou A. (1985): Formation of Singularity and Causality, in A Random Walk in Relativity and Cosmology, ed. by N. Dadhich, J. K. Rao, J. V. Narlikar, C. V. Vishveshwara, Wiley Eastern, New Delhi, pp. 184–191Google Scholar
  82. 82.
    Lake K. (1986): Phys. Lett. A 116, 17MathSciNetADSCrossRefGoogle Scholar
  83. 83.
    Waugh B., Lake K. (1989): Phys. Rev. D 40, 2137MathSciNetADSCrossRefGoogle Scholar
  84. 84.
    Lake K., Zannias T. (1990): Phys. Rev. D. 41, 3866ADSCrossRefGoogle Scholar
  85. 85.
    Christodoulou D. (1993): Relativistic fluids and gravitational collapse, in Global Structure and Evolution in General Relativity, Lecture Notes in Phys. 460, Springer, Berlin Heidelberg New York, pp. 33–54CrossRefGoogle Scholar
  86. 86.
    Iguchi H., Nakao K., Harada T. (1998): Phys. Rev. D 57, 7262MathSciNetADSCrossRefGoogle Scholar
  87. 87.
    Strugackij A., Strugackij B. (1980): Picnic na \( ob\tilde cine \), Molodaja gvardija, MoscowGoogle Scholar

Copyright information

© Springer-Verlag Italia 2000

Authors and Affiliations

  • S. Jhingan
  • G. Magli

There are no affiliations available

Personalised recommendations