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.
Similar content being viewed by others
REFERENCES
Piran, T., ed. (1998). Proc. 8th Marcel Grossmann Meeting (World Scientific, Singapore), to appear.
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).
Yilmaz, H. (1958). Phys. Rev. 111, 1417.
Rosen, N. (1973). Gen. Rel. Grav. 4, 435.
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.
Schweizer, M., and Straumann, N. (1979). Phys. Lett. A 71, 493.
Schweizer, M., Straumann, N., and Wipf, A. (1980). Gen. Rel. Grav. 12, 951.
Rosen, N. (1974). Ann. Phys. (NY) 84, 455.
Yilmaz, H. (1976). Ann. Phys. (NY) 101, 413.
Choquet-Bruhat, Y., DeWitt-Morette, C., and Dillard-Bleick, M. (1982). Analysis, Manifolds and Physics (rev. ed., North-Holland, Amsterdam).
Thirring, W. (1997). Classical Mathematical Physics-Dynamical Systems and Field Theories (3rd. ed. Springer, New York).
Hehl, F. W., McCrea, J. D., Mielke, E. W., and Ne'eman, Y. (1995). Phys. Rep. 258, 1.
Obukhov, Yu. N. (1982). Phys. Lett. B 109, 195.
Obukhov, Yu. N. (1982). Theor. Math. Phys. 50, 229.
Gronwald, F. (1997). Int. J. Mod. Phys. D 6, 263.
Mielke, E. W. (1990). Phys. Rev. D 42, 3388.
Mielke, E. W. (1992). Ann. Phys. (NY) 219, 78.
Hayashi, K., and Shirafuji, T. (1979). Phys. Rev. D 19, 3524.
Wallner, R. P. (1995). J. Math. Phys. 36, 6937.
Rumpf, H. (1978). Z. Naturf. 33a, 1224.
Kopczyński, W. (1982). J. Phys.A 15, 493.
von der Hey de, P. (1976). Z. Naturf. 31a, 1725.
Nitsch, J., and Hehl, F. W. (1980). Phys. Lett. B90, 98.
Synge, J. L. (1971). Relativity: The General Theory (North-Holland, Amsterdam).
Mashhoon, B.: private communication.
Schrüfer, E., Hehl, F. W., and McCrea, J. D. (1987). Gen. Rel. Grav. 19, 197.
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).
Rights and permissions
About this article
Cite this article
Muench, U., Gronwald, F. & Hehl, F.W. A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model. General Relativity and Gravitation 30, 933–961 (1998). https://doi.org/10.1023/A:1026616326685
Issue Date:
DOI: https://doi.org/10.1023/A:1026616326685