General Relativity and Gravitation

, Volume 23, Issue 10, pp 1113–1142 | Cite as

Fluid spacetimes admitting covariantly constant vectors and tensors

  • A. A. Coley
  • B. O. J. Tupper
Research Articles


Spacetimes admitting a covariantly constant vector and satisfying the Einstein field equations for a perfect fluid, a viscous heat-conducting fluid, or an anisotropic fluid are studied. It is found that the only possible perfect fluid spacetimes are the Einstein static universe and ‘stiff-matter’ spacetimes with an isolated spatial co-ordinate, while the possible viscous fluid and anisotropic fluid spacetimes, although more abundant than their perfect fluid counterparts, must satisfy a number of strong restrictions. Examples illustrating most of the various possible situations are given. The paper concludes with a study of covariantly constant second-rank tensors in fluid spacetimes; the only possible solutions that do not also admit a covariantly constant vector are restricted to 2+2 spacetimes.


Field Equation Differential Geometry Viscous Fluid Perfect Fluid Strong Restriction 
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  1. 1.
    Coley, A. A., and Tupper, B. O. J. (1989).J. Math. Phys.,30, 2616.Google Scholar
  2. 2.
    Coley, A. A., and Tupper, B. O. J. (1990).J. Math. Phys.,31, 649.Google Scholar
  3. 3.
    Coley, A. A., and Tupper, B. O. J. (1991). In préparation.Google Scholar
  4. 4.
    Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).Google Scholar
  5. 5.
    Hall, G. S. (1984).Arabian J. Sci. Eng.,9, 88.Google Scholar
  6. 6.
    Kolassis, C. A., Santos, N. O., and Tsoubelis, D. (1988).Class. Quant. Grav.,5, 1329.Google Scholar
  7. 7.
    Wainwright, J., Ince, W. C. W., and Marshman, B. J. (1979).Gen. Rel. Grav.,10, 259.Google Scholar
  8. 8.
    McLenaghan, R. G., Tariq, N., and Tupper, B. O. J. (1975).J. Math. Phys.,16, 829.Google Scholar
  9. 9.
    Hall, G. S., and da Costa, J. (1988).J. Math. Phys.,29, 2465.Google Scholar
  10. 10.
    Tariq, N., and Tupper, B. O. J. (1974).J. Math. Phys.,15, 2232.Google Scholar
  11. 11.
    Tupper, B. O. J. (1981).J. Math. Phys.,22, 2666.Google Scholar
  12. 12.
    Herrera, L., Jimenez, J., Leal, L., Ponce de Léon, J., Esculpi, M., and Galina, V. (1984).J. Math. Phys.,25, 3274.Google Scholar
  13. 13.
    Herrera, L., and Ponce de Léon, J. (1985).J. Math. Phys.,24, 2018.Google Scholar
  14. 14.
    Benton, J. B., and Tupper, B. O. J. (1986).Phys. Rev. D,33, 3534.Google Scholar
  15. 15.
    Misner, C. W. (1968).Astrophys. J.,151, 431.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • A. A. Coley
    • 1
  • B. O. J. Tupper
    • 2
  1. 1.Department of Mathematics, Statistics and Computing ScienceDalhousie UniversityHalifaxCanada
  2. 2.Department of Mathematics and StatisticsUniversity of New BrunswickFrederictonCanada

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