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On the final state of spherical gravitational collapse

  • Published:
Foundations of Physics Letters

Abstract

Following our recent finding [1] that, for the final state of continued spherical gravitational collapse of sufficiently massive bodies, the final gravitational mass of the fluidM ƒ → 0, we show that for a physical fluid the eventual value of 2Mƒ/Rƒ → 1 rather than 2Mƒ/Rƒ2Mƒ/Rƒ < 1 (the speed of light c = 1 and the gravitational constantG = 1), indicating the approach to a zero-mass black hole. We also point out that, as the final state is approached, the curvature components tend to blow up; also the proper radial distancel and the proper time (measured along a radial worldline) Τ → ∞, indicating that actually the singularity is never attained. We also identify that the final state may correspond to the local 3-speed attaining eitherV = 0 orV → c, even though invariant circumference contraction speedU =dR/dΤ → 0. Nonetheless, at a finite observation epoch, such Eternally Collapsing Objects (ECOs) may have a local speed of collapseV≪c and the lab frame speed of collapse may be negligible because of high surface gravitational redshift. However, if quantum back reaction in the strong gravity regime would cause a phase transition of the form pressurep = - ρ, where ρ is the density of the collapsing fluid, it may be possible to have static Ultra Compact Objects (ûCOs) of arbitrary high mass [2]. While supposed Black Holes have no intrinsic magnetic field, ECOs or UCOs are likely to possess strong intrinsic magnetic fields, and we point out that there are already some tentative evidence for existence of such intrinsic magnetic fields in some Black Hole Candidates [3,4]. For the benefit of the readers who may not have gone through Paper I, we also include here the summary of the same. It clearly shows that the central result of Paper I can be derived even without knowing the meaning of the nomenclatureV or without imposing any of property ofV such as whetherV < 1 or not. In addition, we consolidate the same result from other physical considerations too.

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References

  1. A. Mitra.Found. Phys. Lett. 13 (6), 543 (2000), Paper I; astroph/9910408.

    Article  Google Scholar 

  2. P. O. Mazur and E. Mottola,Phys. Rev. Lett, submitted (astroph/0109035).

  3. S. L. Robertson,Astrophys. J. 515, 365 (1999).

    Article  ADS  Google Scholar 

  4. S. L. Robertson and D. Leiter,Astrophys. J. 565, 447 (2002), astro-ph/0102381.

    Article  ADS  Google Scholar 

  5. J. R. Oppenheimer and H. Snyder,Phys. Rev. 56, 455 (1939).

    Article  ADS  Google Scholar 

  6. D. M. Eardley and L. Smarr,Phys. Rev. D 19, 2239 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  7. R. Penrose,Nouvo Cimento 1, 533 (1965).

    Google Scholar 

  8. C. W. Misner and D. H. Sharp,Phys. Rev. 136 2B, 571 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  9. M. May and R. White,Phys. Rev. 141, 1233 (1965).

    MathSciNet  Google Scholar 

  10. C. W. Misner, inAstrophysics and General Relativity, Vol. 1 (Brandeis University Summer School Lectures), M. Chretien, S. Deser, and J. Goldstein, eds. (1968); see pp. 180–181.

  11. C. W. Misner, inRelativity Theory and Astrophysics, Vol. 3, J. Ehlers, ed. (American Mathematical Society, Providence, RI, 1967); see pp. 120–121.

    Google Scholar 

  12. C. W. Misner,Phys. Rev. B 137, 1360 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  13. W. C. Hernandez and C. W. Misner,Astrophys. J. 143, 452 (1966).

    Article  ADS  Google Scholar 

  14. R. W. Lindquist, R. A. Schwartz, and C. W. Misner,Phys. Rev. B 137, 1364 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  15. L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields, 4th edn. (Pergamon, Oxford, 1985).

    MATH  Google Scholar 

  16. S. W. Hawking and G. F. R. Ellis,The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973).

    Book  MATH  Google Scholar 

  17. D. Leiter, A. Mitra, and S. Robertson, astro-ph/0105532.

  18. R. Schoen and S. T. Yau,Commun. Math. Phys.,79, 231 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  19. P. S. Laplace (1799); see English translation in Ref. 15.

  20. A. Einstein,Ann. Math. 40, 922 (1939).

    Article  ADS  Google Scholar 

  21. J. N. Islam,An Introduction to Mathematical Cosmolgy, (Cambridge University Press, Cambridge, 1992).

    Google Scholar 

  22. T. Padmanabhan,Cosmology and Astrophysics Through Problems, (Cambridge University Press, Cambridge, 1996).

    Google Scholar 

  23. C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Pransisco, 1973).

    Google Scholar 

  24. I. Tereno, astro-ph/9905144.

  25. I. Tereno, astro-ph/9905298.

  26. A. Mitra, astro-ph/9905175.

  27. A. Mitra, astro-ph/9905329.

  28. P. Crawford and I. Tereno, gr-qc/0111073.

  29. V. Sabbata, M. Pavsic and E. Recami,Lett. Nuovo Cim.,19, 411 (1977).

    Article  Google Scholar 

  30. L. S. Abrams,Can. J. Phys.,67, 919 (1989); gr-qc/0102055.

    Article  ADS  MathSciNet  Google Scholar 

  31. S. Antoci and D.E. Liebscher, 2001; gr-qc/0102084.

  32. A. Mitra, invited talk given in workshop on Black Holes, Kolkata (2001), organized by Centre for Space Physics (astroph/0105532).

  33. A. Mitra,Bull. Astr. Soc. India,30, 173 (2002), invited talk given in international symposium “Gamma-ray Astrophysics Through Multi-wavelength Experiments,” Mt. Abu, India, 2001.

    ADS  Google Scholar 

  34. K. Schwarzschild,Sitzungsberichte Preuss. Acad. Wiss. 424 (1916).

  35. S. Antoci and A. Loinger, 1999; physics/9905030 and 9912033.

  36. A. Loinger, 2000, astro-ph/0001453, also, 1999, gr-qc/9908009.

  37. Z. Zakir, 1999, gr-qc/9905068.

  38. J. R. Oppenheimer and G. M. Volkoff,Phys. Rev. 55, 374 (1939).

    Article  ADS  Google Scholar 

  39. C. W. Misner and H. S. Zapolsky,Phy. Rev. Lett. 12, 635 (1964).

    Article  ADS  Google Scholar 

  40. P. C. Vaidya,Nature 171, 260 (1953).

    Article  ADS  MathSciNet  Google Scholar 

  41. M. R. Garciaet al. Astrophys. J. 553, L47 (2000); astroph/0012452.

    Article  ADS  Google Scholar 

  42. R. Narayan, M. R. Garcia, and J. E. McClintock, 2001; astroph/0107387.

  43. S. Campana and L. Stella,Astrophys. J. 541, 849 (2000).

    Article  ADS  Google Scholar 

  44. S. V. Vadawale, A. R. Rao, and S. K. Chakrabarti,Astron. Astrophys, in press; 2001 astro-ph/0104378.

  45. K. Menou, astro-ph/0111469.

  46. R. Narayan and J. Heyl, gr-qc/020408.

  47. K. Dev and M. Gleiser (2000), astro-ph/0012265.

  48. J. C. Miller, T. Shahbaz, and L. A. Nolan,Mon. Not. R. Astron. Soc. 294, L25 (1998).

    Article  ADS  Google Scholar 

  49. A. Mitra, in preparation, 2002.

  50. J. R. Laueret al., Astrophys. J. 369, L41 (1991).

    Article  ADS  Google Scholar 

  51. J. Kormendy and D. Richstone,Ann. Rev. Astron. Astrophys. 33, 581 (1995).

    Article  ADS  Google Scholar 

  52. F. Hoyle and W. A. Fowler,Nature 197, 533 (1963).

    Article  ADS  Google Scholar 

  53. W. A. Fowler,Rev. Mod. Phys. 36, 545 (1964).

    Article  ADS  Google Scholar 

  54. E. Agol, 2001,Astrophys. J. Lett, in press; astro-ph/0005051.

  55. D. Dotani, G. Ghisellini, and G . Tagliaferri, 2001,Astron. Astrophys. in press; astro-ph/0105203.

  56. F. Munyaneza and R. D. Viollier,Astrophys. J. 2001, submitted; astro-ph/0103466.

  57. N. Bilic,Phys. Lett. B 515, 105 (2001); astro-ph/0106209.

    Article  ADS  Google Scholar 

  58. A. Svidzinsky, 2001; astro-ph/0105544.

  59. K. Lake,Phys. Rev. Lett. 68, 3192 (1992).

    Article  MathSciNet  Google Scholar 

  60. B. K. Harrison, K. S. Thome, M. Wakano, and J. A. Wheeler,Gravitation Theory and Gravitational Collapse (University Press, Chicago, 1965), p. 75

    Google Scholar 

  61. Ya. B. Zeldovich and I. D. Novikov,Relativistic Astrophysics, Vol. 1, (University Press, Chicago, 1971), p. 297.

    Google Scholar 

  62. F. I. Cooperstock, S. Jhingan, P. S. Joshi, and T. P. Singh,Class. Quan. Grav. 14, 2197 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  63. D. N. Page and S. W. Hawking,Astrophys. J. 206, 1 (1976).

    Article  ADS  Google Scholar 

References

  1. D. F. Torres, S. Capozziello, and G. Lambiase,Phys. Rev. D 62, 104012 (2000); astro-ph/0004064.

    Article  ADS  Google Scholar 

  2. D. F. Torres,Nucl. Phys. B 626, 377 (2002); hep-ph/0201154.

    Article  ADS  Google Scholar 

Download references

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  1. Nuclear Research Laboratory, Bhabha Atomic Research Center, 400085, Mumbai, India

    Abbas Mitra

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Mitra, A. On the final state of spherical gravitational collapse. Found Phys Lett 15, 439–471 (2002). https://doi.org/10.1023/A:1023968113757

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  • DOI: https://doi.org/10.1023/A:1023968113757

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