General Relativity and Gravitation

, Volume 22, Issue 5, pp 539–552 | Cite as

Physical properties of Buchdahl's three-parameter static spherically symmetric perfect fluid metrics

  • Patrick Wils
Research Articles


The physical properties of a static spherically symmetric perfect fluid metric proposed by Buchdahl are investigated. The general solution can be written in terms of associated Legendre functions. If the adiabatic sound speed is to be less than the velocity of light at the boundary of the sphere, its radius will be larger than 1.238 times the Schwarzschild radius. Two particular solutions are studied in detail.


General Solution Differential Geometry Sound Speed Perfect Fluid Legendre Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Buchdahl, H. A. (1959).Phys. Rev.,116, 1027.Google Scholar
  2. 2.
    Finch, M. R., and Skea, J. E. F. (1989).Class. Quant. Grav.,6, 467.Google Scholar
  3. 3.
    Vaidya, P. C., and Tikekar, R. (1982).J. Astrophys. Astron.,3, 325.Google Scholar
  4. 4.
    Abramowitz, M., and Stegun, I. (1965).Handbook of Mathematical Functions (Dover, New York), Ch. 8.Google Scholar
  5. 5.
    Durgapal, M. C., and Bannerji, R. (1983).Phys. Rev. D,27, 328.Google Scholar
  6. 6.
    Knutsen, H. (1984).Astrophys. Space Sci.,98, 207.Google Scholar
  7. 7.
    Knutsen, H. (1988).Mon. Not. R. Astr. Soc,232, 163.Google Scholar
  8. 8.
    Knutsen, H. (1988).Astrophys. Space Sci.,140, 385.Google Scholar
  9. 9.
    Canuto, V. (1975).Ann. Rev. Astron. Astrophys.,13, 335.Google Scholar
  10. 10.
    Arnett, W. D., and Bowers, R. L. (1977).Astrophys. J. Suppl.,33, 415.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Patrick Wils
    • 1
  1. 1.Physics DepartmentUniversitaire Instelling AntwerpenAntwerpenBelgium

Personalised recommendations