Abstract
The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity.
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References
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation, Freeman, San Francisco, California.
Trautman, A. (1958). In Gravitation: An Introduction to Current Research, L. Witten (Eds.), Wiley, New York.
Papapetrou, A. (1951). Proc. R. Ir. Acad. A 25, 11;Bergmann, P. G. and Thompson, R. (1953). Phys. Rev. 89, 400; Landau, L. D. and Lifshitz, E. M. (1962). The Classical Theory of Fields, 2nd Edition, Addison-Wesley, Reading, Massachusetts; Møller, C. (1958). Ann. Phys. 4, 347; Weinberg, S. (1972). Gravitation and Cosmology, Wiley, New York.
Brown, J. D. and York, J. W., Jr. (1993). Phys. Rev. D 47, 1407; Lau, S. (1993). Class. Quant. Grav. 10, 2379; Szabados, L. B. (1994). Class. Quant. Grav. 11, 1847; Hayward, S. A. (1994). Phys. Rev. D 49, 831.
Bergqvist, G. (1992). Class. Quant. Grav. 9, 1917.
Virbhadra, K. S. (1990). Phys. Rev. D 41, 1086;Virbhadra, K. S. (1990). Phys. Rev. D 42, 1066; Virbhadra, K. S. (1990). Phys. Rev. D 42, 2919; Virbhadra, K. S. (1992). Pramana J. Phys. 38, 31; Aguirregabiria, J. M., Chamorro, A., and Virbhadra, K. S. (1996). Gen. Rel. Grav. 28, 1393.
Virbhadra, K. S. (1999). Phys. Rev. D 60, 104041.
Chang, C. C. and Nester, J. M. (1999). Phys. Rev. Lett. 83, 1897.
Tryon, E. P. (1973). Nature 246, 396.
Prigogine, I., Geheniau, J., Gunzing, E., and Nardone, P. (1989). Gen. Rel. Grav. 21, 767.
Cooperstock, F. I. and Israelit, M. (1994). Gen. Rel. Grav. 26, 323.
Rosen, N. (1994). Gen. Rel. Grav. 26, 319.
Garecki, J. (1995). Gen. Rel. Grav. 27, 55; Johri, V. B., Kalligas, D., Singh, P. G., and Everitt, C. W. F. (1995). Gen. Rel. Grav. 27, 313; Feng, S. and Duan, Y. (1996). Chin. Phys. Lett. 13, 409.
Banerjee, N. and Sen, S. (1999). Pramana J. Phys. 49, 609;Radinschi, I. (1999). Acta Phys. Slov. 49, 789; Xulu, S. (2000) Int. J. Theor. Phys. 39, 1153.
Cooperstock, F. I. and Faraoni V. (2003). Astrophys. J. 587, 483.
Gronwald, F. and Hehl, F. W. (1996). In Proc. School of Cosmology and Gravitation on Quantum Gravity, Erice (1995), P. G. Bergmann, V. de Sabbata, and H.-J. Treder (eds.), World Scientific, Singapore;de Andrade, V. C., Guillen, L. C. T., and Pereira, J. G. (2000). In Contribution to the IX Marcel Grossmann Meeting, Rome, Italy, July/2000 (gr-qc/0011087).
Weitzenböck, R. (1923). Invariantentheorie, Noordhoff, Groningen.
Hayashi, K. and Shirafuji, T. (1978). Phys. Rev. D 19, 3524.
de Andrade, V. C. and Pereira, J. G. (1997). Phys. Rev. D 56, 4689.
de Andrade, V. C., Guillen, L. C. T., and Pereira, J. G. (2000). Phys. Rev. Lett. 84, 4533.
Rosen, N. (1958). Phys. Rev. 110, 291.
Rosen, N. and Virbhadra, K. S. (1993). Gen. Rel. Grav. 25, 429;Virbhadra, K. S. (1995). Pramana J. Phys. 45, 215.
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Vargas, T. The Energy of the Universe in Teleparallel Gravity. General Relativity and Gravitation 36, 1255–1264 (2004). https://doi.org/10.1023/B:GERG.0000022386.29438.be
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DOI: https://doi.org/10.1023/B:GERG.0000022386.29438.be