HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 96 (1996) > Number 5
| Next Article >

Prog. Theor. Phys. Vol. 96 No. 5 (1996) pp. 933-947

[ Full Text PDF : FREE ACCESS (693K) ]

Equivalence Principle in the New General Relativity

Takeshi Shirafuji, Gamal G.L. Nashed and Yoshimitsu Kobayashi

Physics Department, Saitama University, Urawa 338

(Received July 22, 1996)

Abstract:

We study the problem of whether the active gravitational mass of an isolated system is equal to the total energy in the tetrad theory of gravitation. The superpotential is derived using the gravitational Lagrangian which is invariant under the parity operation and applied to an exact spherically symmetric solution. Its associated energy is found to be equal to the gravitational mass. The field equation in vacuum is also solved at far distances under the assumption of spherical symmetry. Using the most general expression for parallel vector fields with spherical symmetry, we find that the equality of the gravitational mass and the energy always holds if the parameters of the theory a1, a2 and a3 satisfy the condition (a1 + a2)(a1 - 4a3/9) ≠0. In the two special cases where either (a1 + a2) or (a1 - 4a3/9) is vanishing, however, this equality is not satisfied for the solutions when some components of the parallel vector fields tend to zero as 1/√r for large r.


URL : http://ptp.ipap.jp/link?PTP/96/933/
DOI : 10.1143/PTP.96.933

[ Full Text PDF : FREE ACCESS (693K) ] Citation:

References:

  1. C. M\oller, Mat. Fys. Medd. Dan. Vid. Selsk. 1 (1961), 10.
  2. C. Pellegrini and J. Plebanski, Mat. Fys. Skr. Dan. Vid. Selsk. 2 (1963), 4.
  3. K. Hayashi and T. Nakano, Prog. Theor. Phys. 38 (1967), 491[PTP].
  4. C. M\oller, Mat. Fys. Medd. Dan. Vid. Selsk. 39 (1978), 13.
  5. H. Meyer, Gen. Rev. Grav. 14 (1982), 531.
  6. F. W. Hehl, J. Nitsch and P. Von der Heyde, in General Relativity and Gravitation, ed. A. Held (Plenum Press, New York, 1980), Vol. 1, p. 329.
  7. K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 64 (1980), 866, [PTP]883, 1435, 2222; 65 (1980), 525.
  8. D. Sáez, Phys. Rev. D27 (1983), 2839[APS].
  9. K. Hayashi and T. Shirafuji, Phys. Rev. D19 (1979), 3524[APS]; D24 (1981), 3312.
  10. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. 1928, 217.
  11. S. Miyamoto and T. Nakano, Prog. Theor. Phys. 45 (1971), 295[PTP].
  12. T. Kawai and N. Toma, Prog. Theor. Phys. 83 (1990), 1[PTP].
  13. K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 84 (1990), 36[PTP].
  14. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge U.P., Cambridge, 1993).
  15. K. Nordtvedt, Phys. Rev. 169 (1968), 1014, [APS]1017; 170 (1968), 1186.
  16. J. O. Dickey et al., Science 265 (1994), 482[Science].
  17. J. G. Williams, X. X. Newhall and J. O. Dickey, Phys. Rev. D53 (1996), 6730[APS].
  18. K. Nordtvedt, Icarus 114 (1995), 51.
  19. A. S. Eddington, The Mathematical Theory of Relativity (Cambridge U. P., Cambridge, 1957), p. 105.
  20. H. P. Robertson, in Space Age Astronomy, ed. A. J. Deutsch and W. E. Klemperer (Academic Press, New York, 1962), p. 228.
  21. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 448.
  22. F. I. Mikhail, M. I. Wanas, A. Hindawi and E. I. Lashin, Int. J. Theor. Phys. 32 (1993), 1627.
  23. T. Shirafuji, G. G. L. Nashed and K. Hayashi, Prog. Theor. Phys. 95 (1996), 665[PTP].
  24. C. M\oller, Ann. of Phys. 4 (1958), 347[CrossRef].
  25. H. P. Robertson, Ann. Math. (Princeton) 33 (1932), 496.
  26. F. Müller-Hoissen and J. Nitsch, Phys. Rev. D28 (1983), 718[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 98 No. 6 (1997) pp. 1355-1370 :
    Energy and Momentum in the Tetrad Theory of Gravitation
    Takeshi Shirafuji and Gamal G. L. Nashed
  2. Progress of Theoretical Physics Vol. 99 No. 6 (1998) pp. 971-992 :
    Schwarzschild Space-Time in Gauge Theories of Gravity
    Toshiharu Kawai, Eisaku Sakane and Takashi Tojo
  3. Progress of Theoretical Physics Vol. 104 No. 3 (2000) pp. 505-530 :
    Generalized Equivalence Principle in Extended New General Relativity
    Toshiharu Kawai, Kaoru Shibata and Izumi Tanaka

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.