Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Algebraically special fluid space-times with hypersurface-orthogonal shearfree rays

Abstract

The Einstein field equations are solved subject to the assumptions that (1) the source of the gravitational field is a non-rotating perfect fluid, (2) the Weyl tensor is algebraically special, (3) the repeated principal null direction is tangent to a geodesic, shearfree and twistfree congruence, and is parallely transferred along the fluid congruence. The solutions in which the line-element admits a multiply transitive group of motions have been studied by Stewart and Ellis; the remaining ones are new, and appear to represent inhomogeneous anisotropic cosmological models.

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

References

  1. Doroshkevich, A. G. (1965).Astiofizika 1, 255 [English translation,Astrophysics, 1, 138 (1965)].

  2. Eardley, D., Liang, E. and Sachs, R. (1972).Journal of Mathematical Physics 13, 99.

  3. Eisenhart, L. P. (1961).Continuous Groups of Transformations. Dover Publications Inc., New York.

  4. Ellis, G. F. R. and MacCallum, M. A. H. (1969).Communications in Mathematical Physics 12, 108.

  5. Heckmann, O. and Schucking, E. (1962). InGravitation: An Introduction to Current Research (ed. L. Witten). J. Wiley & Sons, New York.

  6. Jacobs, K. C. (1968).The Astrophysical Journal 153, 661.

  7. Kantowski, R. and Sachs, R. K. (1966).Journal of Mathematical Physics 7, 443.

  8. Kompaneets, A. S. and Chernov, A. S. (1964).Zhurnal éksperimental'noi i teoreticheskoi fiziki,47, 1939 [English translationSoviet Physics JETP,20, 1303 (1965)].

  9. MacCallum, M. A. H. (1971).Communications in Mathematical Physics 20, 57.

  10. Newman, E. T. and Penrose, R. (1962).Journal of Mathematical Physics 3, 556.

  11. Oleson, M. (1971).Journal of Mathematical, Physics 12, 666.

  12. Pirani, F. A. E. (1965). InLectures on General Relativity, Brandeis Summer Institute in Theoretical Physics, Vol. 1. Prentice-Hall, Englewood Cliffs, N.J.

  13. Robinson, I. and Trautman, A. (1962).Proceedings of the Royal Society A265, 463.

  14. Stewart, J. and Ellis, G. F. R. (1968).Journal of Mathematical Physics 9, 1072.

  15. Szekeres, P. (1966).Journal of Mathematical Physics 7, 751.

  16. Thorne, K. S. (1967).The Astrophysical Journal 148, 51.

  17. Trim, D. and Wainwright, J. (1971).Journal of Mathematical Physics 12, 2494.

  18. Vajk, J. P. and Eltgroth, P. G. (1970).Journal of Mathematical Physics 11, 2212.

  19. Wainwright, J. (1970).Communications in Mathematical Physics 17, 42.

  20. Zel'dovich, Ya. B. (1965).Zhurnal éksperimental'no i teoreticheskoi fiziki 48, 98 [English translation,Soviet Physics JETP,21, 656 (1965)].

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wainwright, J. Algebraically special fluid space-times with hypersurface-orthogonal shearfree rays. Int J Theor Phys 10, 39–58 (1974). https://doi.org/10.1007/BF01808315

Download citation

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Field Equation
  • Gravitational Field