Communications in Mathematical Physics

, Volume 58, Issue 3, pp 255–272 | Cite as

Occurrence of whimper singularities

  • S. T. C. Siklos


HOmogeneous space-times (i.e. those admitting a three-parameter group of isometries) are studied using the Newman Penrose formalism. It is found that solutions containing horizons depend on two fewer parameters than the most general solution, so that horizons and the associated whimper singularities are not stable features of homogeneous space-times. In the vacuum case, there are just three two-parameter families with horizons, two of which are the NUT solutions and certain plane waves.


Neural Network Statistical Physic Complex System General Solution Nonlinear Dynamics 
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  1. 1.
    Ellis, G. F. R., Schmidt, B. G.: Singular space-times, submitted to G.R.G.Google Scholar
  2. 2.
    Ellis, G. F. R., King, A. R.: Commun. math. Phys.38, 119 (1974)Google Scholar
  3. 3.
    Clarke, C. J. S., Schmidt, B. G.: G.R.G.8, 129 (1977)Google Scholar
  4. 4.
    Siklos, S. T. C.: to be publishedGoogle Scholar
  5. 5.
    Hawking, S. W., Ellis, G. F. R.: The large scale structure of space-time. Cambridge: Cambridge University Press 1973Google Scholar
  6. 6.
    Ellis, G. F. R., MacCallum, M. A. H.: Commun. math. Phys.12, 108 (1969)Google Scholar
  7. 7.
    King, A. R., Ellis, G. F. R.: Commun. math. Phys.31, 209 (1973)Google Scholar
  8. 8.
    Collins, C. B., Ellis, G. F. R.: Singularities in Bianchi cosmologies. Preprint (1977)Google Scholar
  9. 9.
    Boyer, R. G.: Proc. Roy. Soc. Lond.311, 245 (1969)Google Scholar
  10. 10.
    Siklos, S. T. C.: Preprint, Oxford University (1977)Google Scholar
  11. 11.
    Evans, A. B.: Phys. Lett.55 A, 271 (1975)Google Scholar
  12. 12.
    Penrose, R.: Null hypersurface initial data for classical fields of arbitrary spin and for general relativity. Unpublished dissertationGoogle Scholar
  13. 13.
    Sachs, R. K.: J. Math. Phys.3, 908 (1962)Google Scholar
  14. 14.
    Collins, C. B., Hawking, S. W.: Ap. J.180, 317 (1973)Google Scholar
  15. 15.
    King, A. R.: Phys. Lett.54 A, 115 (1975)Google Scholar
  16. 16.
    Collins, C. B.: Commun. math. Phys.39, 131 (1974)Google Scholar
  17. 17.
    Newman, E., Penrose, R.: J. Math. Phys.3, 566 (1962)Google Scholar
  18. 18.
    Pirani, F. A. E.: Lectures on general relativity, (eds. H. Bondi, F. A. E. Pirani, A. Trautman). Englewood Cliffs. New Jersey: Prentice Hall 1964Google Scholar
  19. 19.
    Reina, C., Treves, A.: G.R.G.7, 817 (1976)Google Scholar
  20. 20.
    Carter, B.: Black hole equilibrium states. In: Black holes (eds. C. DeWitt, B. S. DeWitt). New York: Gordon and Breach 1973Google Scholar
  21. 21.
    Ehlers, J., Kundt, W.: Gravitation: An introduction to current research (ed. L. Witten). New York: Wiley 1962Google Scholar
  22. 22.
    Siklos, S. T. C.: Phys. Lett.59 A, 173 (1977)Google Scholar
  23. 23.
    Siklos, S. T. C.: Unpublished Ph.D. Thesis, Cambridge University (1976)Google Scholar
  24. 24.
    Kasner, E.: Trans. Am. Math. Soc.27, 155 (1925)Google Scholar
  25. 25.
    Taub, A. H.: Ann. Math.53, 472 (1951)Google Scholar
  26. 26.
    Joseph, V.: Proc. Cambridge Phil. Soc.62, 87 (1966)Google Scholar
  27. 27.
    Clarke, C. J. S.: Commun. math. Phys.41, 65 (1975)Google Scholar
  28. 28.
    Kantowski, R., Sachs, R. K.: J. Math. Phys.7, 443 (1966)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • S. T. C. Siklos
    • 1
  1. 1.Department of AstrophysicsUniversity of OxfordOxfordEngland

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