General Relativity and Gravitation

, Volume 19, Issue 2, pp 197–218 | Cite as

Exterior calculus on the computer: The REDUCE-package EXCALC applied to general relativity and to the Poincaré gauge theory

  • Eberhard Schrüfer
  • Friedrich W. Hehl
  • J. Dermott McCrea
Research Articles

Abstract

The computer algebra system REDUCE has recently been enriched by a package on exterior calculus. Here we apply the EXCALC package to the calculation of quantities within the Poincaré gauge theory of gravity, general relativity being included in this scheme as a spcial case. Thereby we simplify and streamline earlier results found by means of tensor-analytical REDUCE calculations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baekler, P., and Hehl, F. W. (1984).Phys. Lett.,A100, 392.Google Scholar
  2. 2.
    Baekler, P., and Hehl, F. W. (1985). InFrom SU(3) to Gravity — Papers in Honour of Yuval Ne'eman, E. Gotsman and G. Tauber, Eds. (Cambridge University Press, Cambridge).Google Scholar
  3. 3.
    Baekler, P., Hehl, F. W., and Mielke, E. W. (1986). InProceedings of the 4th Marcel Grossman Meeting on General Relativity, R. Ruffini, Ed. (North Holland, Amsterdam).Google Scholar
  4. 4.
    Burke, W. L. (1985).Applied Differential Geometry (Cambridge University Press, Cambridge).Google Scholar
  5. 5.
    Choquet-Bruhat, Y., DeWitt-Morette, C., and Dillard-Bleick, M. (1982).Analysis, Manifolds and Physics, rev. ed. (North Holland, Amsterdam).Google Scholar
  6. 6.
    Cohen, I., Frick, I., and Aman, J. E. (1984). InProceedings of the 10th International Conference on General Relativity and Gravitation, B. Bertotti et al., Eds. (Reidel, Dordrecht), p. 139.Google Scholar
  7. 7.
    d'Inverno, R. A. (1980). InGeneral Relativity and Gravitation (One Hundred Years after the Birth of Einstein), A. Held, Ed., Vol. 1 (Plenum Press, New York), p. 491.Google Scholar
  8. 8.
    Edelen, D. G. B. (1981).Programs for Calculation of Isovector Fields in the “Reduce-2” Environment, Report (Lehigh University, Bethlehem, Pennsylvania).Google Scholar
  9. 9.
    Edelen, D. G. B. (1985).Applied Exterior Calculus (Wiley, New York).Google Scholar
  10. 10.
    Ernst, F. J. (1983).Ernst's Equation Evaluator (Program on floppy disk.) (Illinois Institute of Technology, Chicago).Google Scholar
  11. 11.
    Hearn, A. C. (1985).REDUCE User's Manual (Rand Publication CP78. The Rand Corporation, Santa Monica, California 90406).Google Scholar
  12. 12.
    Hehl, F. W. (1980). InProceedings of the 6th Course of the International School of Cosmology and Gravitation on Spin, Torsion and Supergravity. P. G. Bergmann and V. de Sabbata, Eds. (Plenum Press, New York).Google Scholar
  13. 13.
    Hehl, F. W., and McCrea, J. D. (1986).Found. Phys.,16, 267.Google Scholar
  14. 14.
    Kopczynski, W. (1982).J. Phys.,A15, 493.Google Scholar
  15. 15.
    Lovelock, D., and Rund, H. (1975).Tensors, Differential Forms and Variational Principles (Wiley, New York).Google Scholar
  16. 16.
    MacCallum, M. A. H. (1984). InClassical General Relativity, Proceedings of the Conference on Classical (Non-quantum) General Relativity, London, W. B. Bonnor, J. N. Islam, and M. A. H. MacCallum, Eds. (Cambridge University Press, Cambridge), p. 145.Google Scholar
  17. 17.
    McCrea, J. D. (1982).J. Phys.,A15, 1587.Google Scholar
  18. 18.
    McCrea, J. D. (1984).Phys. Lett.,A100, 397.Google Scholar
  19. 19.
    McCrea, J. D. (1984). InClassical General Relativity, W. B. Bonnor, J. N. Islam, and M. A. H. MacCallum, Eds. (Cambridge University Press, Cambridge), p. 173.Google Scholar
  20. 20.
    Mielke, E. W. (1987).Geometrodynamics of Gauge Fields — On the Geometry of Yang-Mills and Gravitational Gauge Theories (Akademie Verlag, Berlin). (In print: English version of Habilitation Thesis, Kiel University, 1982).Google Scholar
  21. 21.
    Schouten, J. A. (1954).Ricci Calculus, 2nd ed. (Springer, Berlin).Google Scholar
  22. 22.
    Schrüfer, E. (1982).SIGSAM Bulletin,16, 27.Google Scholar
  23. 23.
    Schrüfer, E. (1985).EXCALC: A System for Doing Calculations in Modern Differential Geometry, User's Manual (Rand Publication, The Rand Corporation, Santa Monica, California).Google Scholar
  24. 24.
    Schutz, B. (1980).Geometrical Methods of Mathematical Physics (Cambridge University Press, Cambridge).Google Scholar
  25. 25.
    Trautman, A. (1984).Differential Geometry for Physicists, Stony Brook Lectures. (Bibliopolis, Naples).Google Scholar
  26. 26.
    Wallner, R. P. (1983).Acta Phys. Austr.,55, 67.Google Scholar
  27. 27.
    Wallner, R. P. (1985).Gen. Rel. Grav.,17, 1081.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Eberhard Schrüfer
    • 1
  • Friedrich W. Hehl
    • 2
  • J. Dermott McCrea
    • 3
    • 4
  1. 1.Institute F1-P, GMDSt. Augustin 1West Germany
  2. 2.Institute for Theoretical PhysicsUniversity of CologneKöln 41West Germany
  3. 3.Department of Mathematical PhysicsUniversity CollegeDublin 4Ireland
  4. 4.Dublin Institute for Advanced StudiesIreland

Personalised recommendations