Skip to main content
Log in

Finding isometry groups in theory and practice

  • Research Articles
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

An algorithm is given for determining the isometry group of an arbitrary spacetime (in four dimensions). Numerous examples are given and the partial implementation of this algorithm using the symbolic manipulation package CLASSI is discussed.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Karlhede, A., and MacCallum, M. A. H. (1982).Gen. Rel. Grav. 14, 673.

    Google Scholar 

  2. Cartan, E. (1946).Leçons sur la Géométrie des Espaces de Riemann (Gauthier-Villars, Paris).

    Google Scholar 

  3. Brans, C. H. (1965).J. Math. Phys. 6, 94.

    Google Scholar 

  4. Karlhede, A. (1980).Gen. Rel. Grav. 12, 693.

    Google Scholar 

  5. Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry (John Wiley and Sons, New York), vol. 1.

    Google Scholar 

  6. Spivak, M. (1979).A Comprehensive Introduction to Differential Geometry (2nd. ed., Publish or Perish, Houston) vol 2.

    Google Scholar 

  7. Karlhede, A. (1979). “A Review of the Equivalence Problem”, University of Stockholm preprint, Appendices 2 and 3. This paper was later published without the appendices as Ref. 4.

  8. MacCallum, M. A. H., and Skea, J. E. F. (1991). InAlgebraic Computing in General Relativity. Lecture Notes from the First Brazilian School on Computer Algebra, M. J. Rebouças and W. L. Roque, eds. (Oxford University Press, Oxford), vol. 2, to appear.

    Google Scholar 

  9. Schmidt, B. (1968). Dissertation, Universität Hamburg.

  10. 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 

  11. MacCallum, M. A. H. (1980). “On Enumerating the Real Four Dimensional Lie Algebras”, Queen Mary College preprint.

  12. Kruchkovich, G. I. (1954).Usp. Matem. Nauk SSSR, 9, part 1(59), 3; Petrov, A. Z. (1969).Einstein Spaces (Pergamon, Oxford); Bratzlavsky, F. (1959).Sur les algèbres et les groupes de Lie résolubles de dimension trois et quatre. Memoire de Licence, Université Libre de Bruxelles; Mubarakzyanov, G. M. (1963).Izv. Vyss. Uch. Zav. Mat. 1(32), 114;3(34), 99;4(35), 104; Patera, J., Sharp, R. T., Winternitz, P., and Zassenhaus, H. (1976).J. Math. Phys. 17, 986.

    Google Scholar 

  13. Gott III, J. R. (1985).Astrophys. J. 288, 422.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Araujo, M.E., Dray, T. & Skea, J.E.F. Finding isometry groups in theory and practice. Gen Relat Gravit 24, 477–500 (1992). https://doi.org/10.1007/BF00760132

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00760132

Keywords

Navigation