Communications in Mathematical Physics

, Volume 31, Issue 3, pp 209–242

Tilted homogeneous cosmological models

  • A. R. King
  • G. F. R. Ellis
Article

Abstract

We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.

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References

  1. 1.
    Ellis, G. F. R., MacCallum, M. A. H.: Commun. math. Phys.12, 108 (1969).Google Scholar
  2. 2.
    MacCallum, M. A. H., Ellis, G. F. R.: Commun. math. Phys.19, 31 (1970).Google Scholar
  3. 3.
    MacCallum, M. A. H.: Commun. math. Phys.20, 57 (1971).Google Scholar
  4. 4.
    Heckmann, O., Schücking, E.: Relativistic Cosmology, in Gravitation, ed. L. Witten 438. New York: Wiley 1962.Google Scholar
  5. 5.
    Estabrook, F. B., Wahlquist, H. D., Behr, C. G.: J. Math. Phys.9, 497 (1968).Google Scholar
  6. 6.
    Ozsváth, I.: J. Math. Phys.11, 2860 (1970).Google Scholar
  7. 7.
    Ehlers, J.: Akad. Wiss. u. Lit. (Mainz), Abh. Math. Nat. Kl. No 11 (1961).Google Scholar
  8. 8.
    Ellis, G. F. R.: Relativistic Cosmology, in General Relativity and Cosmology, ed. R. K. Sachs, XLVII Enrico Fermi Summer School proceedings 104. New York: Academic Press 1971.Google Scholar
  9. 9.
    Schouten, J. A.: Ricci Calculus. Berlin-Göttingen-Heidelberg: Springer 1954.Google Scholar
  10. 10.
    Schmidt, B. G.: article in proceedings of Banff Summer School, 1972.Google Scholar
  11. 11.
    Gödel, K.: Proc. Int. Math. Cong. (Camb., Mass)1, 175, (Am. Math. Soc. Providence), (1952).Google Scholar
  12. 12.
    Ellis, G. F. R.: J. Math. Phys.8, 1171 (1967).Google Scholar
  13. 13.
    Stewart, J. M., Ellis, G. F. R.: J. Math. Phys.9, 1072 (1968).Google Scholar
  14. 14.
    Ozsváth, I.: J. Math. Phys.12, 1078 (1971).Google Scholar
  15. 15.
    Collins, C. B., Hawking, S. W.: Astrophys. J.180, 317 (1973).Google Scholar
  16. 16.
    Farnsworth, D. L.: J. Math. Phys.8, 2315 (1967).Google Scholar
  17. 17.
    Demianski, M., Grischuk, L. P.: Commun. math. Phys.25, 233 (1972).Google Scholar
  18. 18.
    Hawking, S. W.: Mon. Not. Roy. Ast. Soc.142, 129 (1969).Google Scholar
  19. 19.
    Matzner, R. A.: Astrophys. J.157, 1085 (1969).Google Scholar
  20. 20.
    Shepley, L.: Ph. D. Thesis, Princeton University (1965); Proc. Nat. Acad. Sci.52, 1403 (1964).Google Scholar
  21. 20 a.
    Matzner, R. A., Shepley, L. C., Warren, J. A.: Ann. Phys. (N. Y.)57, 401 (1970).Google Scholar
  22. 21.
    Matzner, R. A.: J. Math. Phys.11, 2432 (1970);13, 931 (1972); Ann. Phys. (N.Y.)65, 438, 482 (1971).Google Scholar
  23. 21 a.
    Matzner, R. A., Chitre, D. M.: Commun. math. Phys.22, 173 (1971).Google Scholar
  24. 21 b.
    Matzner, R. A., Misner, C. W.: Astrophys. J.171, 415, 433 (1972).Google Scholar
  25. 22.
    Ryan, M. P.: J. Math. Phys.10, 1724 (1969); Ann. Phys.65, 506 (1971);68, 541 (1971);70, 301 (1972).Google Scholar
  26. 23.
    Belinskii, V. A., Khalatnikov, I. M., Lifshitz, E. M.: Z.E.T.F.60, 1969 (1971).Google Scholar
  27. 23 a.
    Grischuk, L. P., Doroshkevich, A. G., Lukash, V. N.: Z.E.T.F.61, 3 (1971).Google Scholar
  28. 24.
    Grischuk, L. P., Doroshkevich, A. G., Novikov, I. D.: Z.E.T.F.55, 2281 (1968); (Sov. Phys. J.E.T.P.28, 1214 (1969)).Google Scholar
  29. 25.
    Ruzmaikina, T. V., Ruzmaikin, A. A.: Z.E.T.F.56, 1742 (1969); (Sov. Phys. J.E.T.P.29, 934 (1969)).Google Scholar
  30. 26.
    Ozsváth, I.: J. Math. Phys.6, 590 (1965).Google Scholar
  31. 27.
    Farnsworth, D. L., Kerr, R. P.: J. Math. Phys.7, 1625 (1966).Google Scholar
  32. 28.
    Schücking, E.: Naturwissen.19, 507 (1957).Google Scholar
  33. 29.
    Banerji, S.: Prog. Theor. Phys.39, 365 (1968).Google Scholar
  34. 30.
    Ozsváth, I., Schücking, E.: Ann. Phys. (N.Y.),55, 166 (1969).Google Scholar
  35. 31.
    Gödel, K.: Rev. Mod. Phys.21, 447 (1949).Google Scholar
  36. 32.
    King, A. R.: Ph. D. Thesis, University of Cambridge, in preparation.Google Scholar
  37. 33.
    Kantowski, R., Sachs, R. K.: J. Math. Phys.7, 443 (1966).Google Scholar
  38. 34.
    Taub, A. H.: Proceedings of the 1967 Colloque on «Fluids et champ gravitationnel en relativité générale», No. 170, 57, Paris: Centre National de la Recherche Scientifique (1969).Google Scholar
  39. 35.
    MacCallum, M. A. H., Taub, A. H.: Commun. math. Phys.25, 173 (1972).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • A. R. King
    • 1
  • G. F. R. Ellis
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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