International Journal of Theoretical Physics

, Volume 33, Issue 4, pp 967–982 | Cite as

Junction conditions and static fluid cylinders in Lyra's geometry

  • Jerzy Matyjasek
Article

Abstract

Junction conditions for Sen's theory in Lyra's geometry are considered. It is proposed that for any gauge function the standard O'Brien-Synge and Lichnerowicz junction conditions should be supplemented by demanding continuity of the displacement vector across the interface. A class of internal solutions of the Sen equations with a source term given by the energy-momentum tensor of a one-component perfect fluid with the ultrarelativistic equation of state that is expressible in terms of Bessel functions is proposed. The internal solution is regularly matched by means of the junction conditions to the exterior solution. The resulting two-parameter solution is globally non-Euclidean.

Keywords

Field Theory Elementary Particle Quantum Field Theory Bessel Function Source Term 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beesham, A. (1986a).Astrophysics and Space Science,127, 189.Google Scholar
  2. Beesham, A. (1986b).Astrophysics and Space Science,127, 355.Google Scholar
  3. Beesham, A. (1988).Australian Journal of Physics,41, 833.Google Scholar
  4. Bhamra, K. S. (1974).Australian Journal of Physics,27, 541.Google Scholar
  5. Bonnor, W. B. (1979).Journal of Physics A,12, 8746.Google Scholar
  6. Bonnor, W. B. (1982).General Relativity and Gravitation,14, 807.Google Scholar
  7. Evans, A. B. (1977).Journal of Physics A,10, 1303.Google Scholar
  8. Halford, W. D. (1970).Australian Journal of Physics,23, 863.Google Scholar
  9. Halford, W. D. (1972).Journal of Mathematical Physics,13, 1699.Google Scholar
  10. Hoyle, F., and Narlikar, J. V. (1948).Monthly Notices of the Royal Astronomical Society,108, 372.Google Scholar
  11. Israel, W. (1958).Proceedings of the Royal Society A,248, 404.Google Scholar
  12. Israel, W. (1966).Nuovo Cimento,44B, 1.Google Scholar
  13. Lichnerowicz, A. (1955).Theories Relativistes de la Gravitation et de l'Electromagnetisme, Masson, Paris.Google Scholar
  14. Lyra, G. (1951).Mathematische Zeitschrift,54, 52.Google Scholar
  15. Marder, L. (1958).Proceedings of the Royal Society A.244, 524.Google Scholar
  16. Matyjasek, J., and Rogatko, M. (1992).Astrophysics and Space Science,192, 299.Google Scholar
  17. Nariai, H. (1965).Progress of Theoretical Physics,34, 173.Google Scholar
  18. O'Brien, S., and Synge, J. L. (1952).Communications of the Institute for Advanced Studies,A9. Google Scholar
  19. Ram, S., and Singh, P. (1992).International Journal of Theoretical Physics,31, 2095.Google Scholar
  20. Scheibe, E. (1952).Mathematische Zeitschrift,57, 65.Google Scholar
  21. Sen, D. K. (1957).Zeitschrift für Physik,149, 311.Google Scholar
  22. Sen, D. K. (1960).Canadian Mathematical Bulletin,5, 255.Google Scholar
  23. Sen, D. K. (1968).Fields and/or Particles, Academic Press, New York.Google Scholar
  24. Sen, D. K., and Dunn, K. A. (1971).Journal of Mathematical Physics,12, 578.Google Scholar
  25. Sen, D. K., and Vanstone, J. R. (1972).Journal of Mathematical Physics,13, 990.Google Scholar
  26. Singh, T., and Agrawal, A. K. (1992).International Journal of Theoretical Physics,31, 575.Google Scholar
  27. Singh, T., and Singh, G. P., (1991).Journal of Mathematical Physics,32, 2456.Google Scholar
  28. Singh, T., and Singh, G. P. (1992).International Journal of Theoretical Physics,31, 1433.Google Scholar
  29. Soleng, H. H. (1987).General Relativity and Gravitation,19, 1213.Google Scholar
  30. Spivak, M. (1979).A Comprehensive Introduction to Differential Geometry, Publish or Perish, Berkeley, California.Google Scholar
  31. Synge, J. L. (1960).Relativity: The General Theory, North-Holland, Amsterdam.Google Scholar
  32. Weyl, H. (1918).Annalen der Physik,1918, 465.Google Scholar
  33. Weyl, H. (1921).Göttinger Nachrichten,1921, 99.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Jerzy Matyjasek
    • 1
  1. 1.Institute of PhysicsMaria Curie-Skłodowska UniversityLublinPoland

Personalised recommendations