General Relativity and Gravitation

, Volume 27, Issue 4, pp 367–378 | Cite as

Dark matter and non-newtonian gravity from general relativity coupled to a fluid of strings

  • Harald H. Soleng
Article

Abstract

An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a 1/r correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.

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References

  1. 1.
    Letelier, P. (1979).Phys. Rev. D 20, 1294.Google Scholar
  2. 2.
    Letelier, P. (1981).Nuovo Cimento 63B, 519.Google Scholar
  3. 3.
    Vilenkin, A. (1984).Phys. Rev. Lett. 53, 1016.Google Scholar
  4. 4.
    Gott, J. R. (1985).Astrophys. J. 288, 422.Google Scholar
  5. 5.
    Hiscock, W. A. (1985).Phys. Rev. D 31, 3288.Google Scholar
  6. 6.
    Gott, J. R. (1991).Phys. Rev. D 66, 1126.Google Scholar
  7. 7.
    Kabat, D. N. (1992).Phys. Rev. D 46, 2720.Google Scholar
  8. 8.
    Soleng, H. H. (1990).Astron. Astrophys. 237, 1.Google Scholar
  9. 9.
    Petrov, A. Z. (1969).Einstein Spaces (Pergamon Press, Oxford).Google Scholar
  10. 10.
    Gliner, É. B. (1966).Sov. Phys. JETP 22, 378.Google Scholar
  11. 11.
    Dymnikova, I. (1992).Gen. Rel. Grav. 24, 235.Google Scholar
  12. 12.
    Soleng, H. H. (1994).Gen. Rel. Grav. 26, 149.Google Scholar
  13. 13.
    Sancisi, R., and van Albada, T. S. (1987). InDark Matter in the Universe. 117th IAU symposium H. Kormendy and G. R. Knapp, eds. (D. Reidel Publishing Co., Dordrecht, Holland).Google Scholar
  14. 14.
    Battaner, E., Garrido, J. L., Membrado, M., and Florido, B. (1992).Nature 360, 652.Google Scholar
  15. 15.
    Finzi, A. (1963).Mon. Not. R. Astr. Soc. 127, 21.Google Scholar
  16. 16.
    Milgrom, M. (1983).Astrophys. J. 270, 365.Google Scholar
  17. 17.
    Bekenstein J., and Milgrom, M. (1984).Astrophys. J. 286, 7.Google Scholar
  18. 18.
    Kuhn J. R., and Kruglyak, L. (1987).Astrophys. J. 313, 1.Google Scholar
  19. 19.
    Sanders, R. H. (1990).Astron. Astrophys. Rev. 2, 1.Google Scholar
  20. 20.
    Liboff, R. L. (1992).Astrophys. J. Lett. 397, L71.Google Scholar
  21. 21.
    Milgrom, M. (1987). InDark Matter in the Universe. Proc. 4th Jerusalem Winter School for Theoretical Physics, J. N. Bahcall, T. Piran and S. Weinberg, eds. (World Scientific, Singapore).Google Scholar
  22. 22.
    Milgrom, M., and Bekenstein, J. (1987). InDark Matter in the Universe. 117th IAU symposium H. Kormendy and G. R. Knapp, eds. (D. Reidel Publishing Co., Dordrecht, Holland).Google Scholar
  23. 23.
    Milgrom, M. (1989).Comm. Astrophys. 13, 215.Google Scholar
  24. 24.
    Milgrom, M. (1983).Astrophys. J. 270, 371.Google Scholar
  25. 25.
    Milgrom, M. (1984).Astrophys. J. 287, 571.Google Scholar
  26. 26.
    Milgrom, M. (1986).Astrophys. J. 302, 617.Google Scholar
  27. 27.
    Milgrom, M. (1983).Astrophys. J. 270, 384.Google Scholar
  28. 28.
    Begeman, K. G., Broeils, A. H., and Sanders, R. H. (1991).Mon. Not. R. Astron. Soc. 249, 523.Google Scholar
  29. 29.
    Lake, G. (1989).Astrophys. J. 345, L17.Google Scholar
  30. 30.
    Milgrom, M. (1991).Astrophys. J. 367, 490.Google Scholar
  31. 31.
    Gerhard, O. E., and Spergel, D. N. (1992).Astrophys. J. 397, 38.Google Scholar
  32. 32.
    Tohline, J. E. (1983). InInternal Kinematics and Dynamics of Galaxies. 100th IAU symposium, A. Athanassoula, ed. (D. Reidel Publishing Co., Dordrecht, Holland).Google Scholar
  33. 33.
    Lindley, D. (1992).Nature 359, 583.Google Scholar
  34. 34.
    Bekenstein, J. (1988). InProc. 2nd Canadian Conference on General Relativity and Relativistic Astrophysics, A. Coley, C. Dyer, B. Tupper, eds. (World Scientific, Singapore).Google Scholar
  35. 35.
    Bekenstein, J. (1988).Phys. Lett. B202, 497.Google Scholar
  36. 36.
    Bekenstein, J. (1990). InDevelopments in General Relativity, Astrophysics and Quantum Theory: A Jubilee Volume in Honour of Nathan Rosen, P. Cooperstock, L. P. Horwitz and J. Rosen, eds. (IOP, Bristol, U.K.).Google Scholar
  37. 37.
    Bekenstein, J. (1992). InProc. VI Marcel Grossman Meeting, Kyoto, 1991, H. Sato and T. Nakamura, eds. (World Scientific, Singapore).Google Scholar
  38. 38.
    Ishizawa, T. (1987). InDark Matter in the Universe. 117th IAU symposium, H. Kormendy and G. R. Knapp, eds. (D. Reidel Publishing Co., Dordrecht, Holland).Google Scholar
  39. 39.
    Vilenkin, A. (1985).Phys. Rep. 121, 263.Google Scholar
  40. 40.
    Gott, J. R., and Rees, M. J. (1987).Mon. Not. R. Astr. Soc. 277, 453.Google Scholar
  41. 41.
    Tully, R. B., and Fisher, J. R. (1977).Astron. Astrophys. 54, 661.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Harald H. Soleng
    • 1
  1. 1.NORDITACopenhagen ØDenmark

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