Skip to main content
SpringerLink
Log in

Collapsing shear-free perfect fluid spheres with heat flow

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. The formulas for the characteristics of the model are straight and tractable. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time-dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Herrera L., Di Prisco A., Ospino J.: Phys. Rev. D 74, 044001 (2006)

    Article  ADS  Google Scholar 

  2. Santos N.O.: Mon. Not. R. Astron. Soc. 216, 403 (1985)

    ADS  Google Scholar 

  3. Krasinski A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  4. Bonnor W.B., De Oliveira A.K.G., Santos N.O.: Phys. Rep. 5, 269 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  5. Kustanheimo P., Qvist B.: Comm. Phys. Math. Helsingf. 13, 16 (1948)

    Google Scholar 

  6. Glass E.N.: J. Math. Phys. 20, 1508 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  7. Stephani H., Kramer D., Maccalum M., Hoenselaers C., Herlt E.: Exact Solutions to Einstein’s Field Equations. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  8. Ivanov B.V.: Int. J. Mod. Phys. A 25, 3975 (2010)

    Article  ADS  MATH  Google Scholar 

  9. Ivanov B.V.: Int. J. Mod. Phys. D 20, 319 (2011)

    Article  ADS  MATH  Google Scholar 

  10. Msomi A.M., Govinder K.S., Maharaj S.D.: Gen. Relativ. Gravit. 43, 1685 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Msomi A.M., Govinder K.S., Maharaj S.D.: Int. J. Theor. Phys. 51, 1290 (2012)

    Article  Google Scholar 

  12. Kuchowicz B.: Phys. Lett. A 35, 223 (1971)

    Article  ADS  Google Scholar 

  13. Kuchowicz B.: Acta Phys. Pol. B 3, 209 (1972)

    Google Scholar 

  14. Goldman S.P.: Astrophys. J. 226, 1079 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  15. Stewart B.V.: J. Phys. A 15, 1799 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  16. Knutsen H.: Gen. Relativ. Gravit. 23, 843 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  17. Rahman S., Visser M.: Class. Quantum Grav. 19, 935 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Lake K.: Phys. Rev. D 67, 104015 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  19. Herrera L., Le Denmat G., Santos N.O., Wang A.: Int. J. Mod. Phys. D 13, 583 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Maharaj S.D., Govender M.: Int. J. Mod. Phys. D 14, 667 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Mishtry S.S., Maharaj S.D., Leach P.G.L.: Math. Meth. Appl. Sci. 31, 363 (2008)

    Article  Google Scholar 

  22. De Oliveira A.K.G., Santos N.O., Kolassis C.A.: Mon. Not. R. Astron. Soc. 216, 1001 (1985)

    ADS  MATH  Google Scholar 

  23. De Oliveira A.K.G., De Pacheco J.A.F., Santos N.O.: Mon. Not. R. Astron. Soc. 220, 405 (1986)

    ADS  MATH  Google Scholar 

  24. De Oliveira A.K.G., Kolassis C.A., Santos N.O.: Mon. Not. R. Astron. Soc. 231, 1011 (1988)

    ADS  Google Scholar 

  25. Banerjee A., Chatterjee S., Dadhich N.: Mod. Phys. Lett. A 17, 2335 (2002)

    Article  ADS  MATH  Google Scholar 

  26. Herrera L., Ospino J., Di Prisco A., Fuenmayor E., Troconis O.: Phys. Rev. D 79, 064025 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  27. Govender M., Maharaj S.D., Maartens R.: Class. Quantum Grav. 15, 323 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Govender M., Maartens R., Maharaj S.D.: Mon. Not. R. Astron. Soc. 310, 557 (1999)

    Article  ADS  Google Scholar 

  29. Govinder K.S., Govender M.: Phys. Lett. A 283, 71 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Pinheiro G., Chan R.: Gen. Relativ. Gravit. 40, 2149 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Joshi P.S., Malafarina D., Narayan R.: Class. Quantum Grav. 28, 235018 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  32. Kuchowicz B.: Acta Phys. Pol. B 4, 415 (1973)

    Google Scholar 

  33. Buchdahl H.A.: Aust. J. Phys. 9, 13 (1956)

    MathSciNet  ADS  MATH  Google Scholar 

  34. Glass E.N.: Phys. Lett. A 86, 351 (1981)

    Article  ADS  Google Scholar 

  35. Banerjee A., Chatterjee S.: Astrophys. Space Sci. 299, 219 (2005)

    Article  ADS  MATH  Google Scholar 

  36. Govinder K.S., Govender M.: Gen. Relativ. Gravit. 44, 147 (2012)

    Article  ADS  MATH  Google Scholar 

  37. Banerjee A., Dutta Choudhury S.B., Bhui B.K.: Phys. Rev. D 40, 670 (1989)

    Article  ADS  Google Scholar 

  38. Gürses M., Gürsey Y.: Nuovo Cim. B 25, 786 (1975)

    Article  ADS  Google Scholar 

  39. Kramer D.: J. Math. Phys. 33, 1458 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Maharaj S.D., Govender M.: Aust. J. Phys. 50, 959 (1997)

    ADS  MATH  Google Scholar 

  41. Strobel H.: Jena. Math. Naturw. Reihe 17, 195 (1968)

    Google Scholar 

  42. Maiti S.R.: Phys. Rev. D 25, 2518 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  43. Sanyal A.K., Ray D.: J. Math. Phys. 25, 1975 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  44. Modak B.: J. Astrophys. Astr. 5, 317 (1984)

    Article  ADS  Google Scholar 

  45. Deng Y.: Gen. Relativ. Gravit. 21, 503 (1989)

    Article  ADS  Google Scholar 

  46. Deng Y., Mannheim P.D.: Phys. Rev. D 42, 371 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  47. Som M.M., Santos N.O.: Phys. Lett. A 87, 89 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  48. Thirukkanesh S., Maharaj S.D.: J. Math. Phys. 50, 022502 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  49. Kolassis C.A., Santos N.O., Tsoubelis D.: Astrophys. J. 327, 755 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  50. Chan R., Lemos J., Santos N.O., De Pacheco J.A.F.: Astrophys. J. 342, 976 (1989)

    Article  ADS  Google Scholar 

  51. Grammenos T.: Astrophys. Space Sci. 211, 31 (1994)

    Article  ADS  MATH  Google Scholar 

  52. Bergmann O.: Phys. Lett. A 82, 383 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  53. Jiang S.: J. Math. Phys. 33, 3503 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. Nariai H.: Prog. Theor. Phys. 38, 92 (1967)

    Article  ADS  Google Scholar 

  55. Buchdahl H.A.: Astrophys. J. 140, 1512 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  56. Bayin S.: Phys. Rev. D 18, 2745 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  57. Narlikar V.V., Patwardhan G.K., Vaidya P.C.: Proc. Nat. Inst. Sci. India 9, 229 (1943)

    MathSciNet  MATH  Google Scholar 

  58. Nariai H.: Sci. Rep. Tohoku Univ. 34, 160 (1950)

    MathSciNet  ADS  Google Scholar 

  59. Kuchowicz B.: Indian J. Pure Appl. Math. 2, 297 (1971)

    MathSciNet  ADS  MATH  Google Scholar 

  60. Pant D.N., Sah A.: Phys. Rev. D 32, 1358 (1985)

    Article  ADS  Google Scholar 

  61. Banerjee A., Dutta Choudhury S.B., Bhui B.K.: Pramana 34, 397 (1990)

    Article  ADS  Google Scholar 

  62. Burlankov D.E.: Theor. Math. Phys. 95, 455 (1993)

    Article  MathSciNet  Google Scholar 

  63. Pant N., Mehta R.N., Pant M.J.: Astrophys. Space Sci. 330, 353 (2010)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Science, Tzarigradsko Shausse 72, 1784, Sofia, Bulgaria

    B. V. Ivanov

Authors
  1. B. V. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. V. Ivanov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, B.V. Collapsing shear-free perfect fluid spheres with heat flow. Gen Relativ Gravit 44, 1835–1855 (2012). https://doi.org/10.1007/s10714-012-1370-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-012-1370-3

Keywords

Search

Navigation