Advertisement

General Relativity and Gravitation

, Volume 30, Issue 6, pp 933–961 | Cite as

A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

  • Uwe Muench
  • Frank Gronwald
  • Friedrich W. Hehl
Article

Abstract

Recently Kaniel and Itin proposed a gravitational model with the wave type equation \(\left[ { + \lambda \left( x \right)} \right]\vartheta ^\alpha = 0\) as vacuum field equation, where \(\vartheta ^\alpha\) denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.

GRAVITY GAUGE THEORY TELEPARALLELISM VARIATION HODGE DUALS 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Piran, T., ed. (1998). Proc. 8th Marcel Grossmann Meeting (World Scientific, Singapore), to appear.Google Scholar
  2. 2.
    Kaniel, S., and Itin, Y. (1997) “Gravity on a parallelizable manifold”, Los Alamos eprint archive gr-qc/9707008 (presented at the 8th Marcel Grossmann Meeting in Jerusalem).Google Scholar
  3. 3.
    Yilmaz, H. (1958). Phys. Rev. 111, 1417.Google Scholar
  4. 4.
    Rosen, N. (1973). Gen. Rel. Grav. 4, 435.Google Scholar
  5. 5.
    Gronwald, F. and Hehl, F. W. (1996). In Proc. Int., School of Cosmology and Gravitation. 14th Course: Quantum Gravity (May 1995, Erice, Italy), P.G. Bergmann et al., eds. (World Scientific, Singapore), p.148-198; Los Alamos eprint archive grqc/9602013.Google Scholar
  6. 6.
    Schweizer, M., and Straumann, N. (1979). Phys. Lett. A 71, 493.Google Scholar
  7. 7.
    Schweizer, M., Straumann, N., and Wipf, A. (1980). Gen. Rel. Grav. 12, 951.Google Scholar
  8. 8.
    Rosen, N. (1974). Ann. Phys. (NY) 84, 455.Google Scholar
  9. 9.
    Yilmaz, H. (1976). Ann. Phys. (NY) 101, 413.Google Scholar
  10. 10.
    Choquet-Bruhat, Y., DeWitt-Morette, C., and Dillard-Bleick, M. (1982). Analysis, Manifolds and Physics (rev. ed., North-Holland, Amsterdam).Google Scholar
  11. 11.
    Thirring, W. (1997). Classical Mathematical Physics-Dynamical Systems and Field Theories (3rd. ed. Springer, New York).Google Scholar
  12. 12.
    Hehl, F. W., McCrea, J. D., Mielke, E. W., and Ne'eman, Y. (1995). Phys. Rep. 258, 1.Google Scholar
  13. 13.
    Obukhov, Yu. N. (1982). Phys. Lett. B 109, 195.Google Scholar
  14. 14.
    Obukhov, Yu. N. (1982). Theor. Math. Phys. 50, 229.Google Scholar
  15. 15.
    Gronwald, F. (1997). Int. J. Mod. Phys. D 6, 263.Google Scholar
  16. 16.
    Mielke, E. W. (1990). Phys. Rev. D 42, 3388.Google Scholar
  17. 17.
    Mielke, E. W. (1992). Ann. Phys. (NY) 219, 78.Google Scholar
  18. 18.
    Hayashi, K., and Shirafuji, T. (1979). Phys. Rev. D 19, 3524.Google Scholar
  19. 19.
    Wallner, R. P. (1995). J. Math. Phys. 36, 6937.Google Scholar
  20. 20.
    Rumpf, H. (1978). Z. Naturf. 33a, 1224.Google Scholar
  21. 21.
    Kopczyński, W. (1982). J. Phys.A 15, 493.Google Scholar
  22. 22.
    von der Hey de, P. (1976). Z. Naturf. 31a, 1725.Google Scholar
  23. 23.
    Nitsch, J., and Hehl, F. W. (1980). Phys. Lett. B90, 98.Google Scholar
  24. 24.
    Synge, J. L. (1971). Relativity: The General Theory (North-Holland, Amsterdam).Google Scholar
  25. 25.
    Mashhoon, B.: private communication.Google Scholar
  26. 26.
    Schrüfer, E., Hehl, F. W., and McCrea, J. D. (1987). Gen. Rel. Grav. 19, 197.Google Scholar
  27. 27.
    Stauffer, D., Hehl, F. W., Ito, N., Winkelmann, V. and Zabolitzky, J. G. (1993). Computer Simulation and Computer Algebra-Lectures for Beginners (3rd. ed., Springer, Berlin).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Uwe Muench
  • Frank Gronwald
  • Friedrich W. Hehl

There are no affiliations available

Personalised recommendations