Self-dual Lorentzian wormholes and energy in teleparallel theory of gravity

Gamal G. L. Nashed1

Abstract

Two spherically symmetric, static Lorentzian wormholes are obtained in tetrad theory of gravitation as a solution of the equation r = rt = 0, where r = Tijuiuj, rt = (Tij-[ 1/2]Tgij)uiuj and uiui = -1. This equation characterizes a class of spacetime which are ßelf-dual" (in the sense of electrogravity duality). The obtained solutions are characterized by two parameters k1 and k2 and have a common property that they reproduce the same metric spacetime. This metric describes a static Lorentzian wormhole and includes the Schwarzschild black hole as a special case. Calculating the energy content of these tetrad fields using Møller's superpotential method in the context of teleparallel spacetime, we find that E = m or 2m, which does not depend on the two parameters k1 and k2 that characterize the wormhole.

References

  1. L. Flamm, Phys. Z. 17, 48 (1916).
  2. M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).
  3. M. S. Morris, K.S. Thorne, and U. Yurtsever, Phys. Rev. Lett. 61, 1446 (1988).
  4. I. D. Novikov, Sov. Phys. JETP 68, 439 (1989).
  5. M. Visser, Lorentzian Wormholes-From Einstein to Hawking (American Institute of Physics, New York, 1996).
  6. P. K. F. Kuhfittig, Phys. Rev. D 67, 064015 (2003).
  7. T. A. Roman, Phys. Rev. D 47, 1370 (1993).
  8. H. Epstein, E. Glaser, and A. Yaffe, Nuovo Cim. 36, 2296 (1965).
  9. M. Visser and D. Hochberg, Geometric Wormhole Throats, in: The Internal Structure of Black Holes and Spacetime Singularities (Haifa, Israel, June-July 1997), gr-qc/9710001.
  10. D. Hochberg, Phys. Lett. B 251 349 (1990); B. Bhawal and S. Kar, Phys. Rev. D 46, 2464 (1992).
  11. S. Kar, Phys. Rev. D 49, 862 (1994); S. Kar and D. Sahdev, Phys. Rev. D 53, 722 (1996).
  12. D. Hochberg and M. Visser, Phys. Lett. 81, 764 (1998); Phys. Rev. D 58, 044021 (1998).
  13. N. Dadhich, S. Kar, S. Mukherjee and M. Visser, Phys. Rev. D65, 064004 (2002).
  14. D. Hochberg and M. Visser, General dynamic wormholes and violation of the null energy condition, in: Advanced School on Cosmology and Particle Physics, Spain, 22-28 June (1998); gr-qc/9901020.
  15. C. Moller, Mat. Fys. Medd. Dan. Vid. Selsk. 39, 13 (1978).
  16. C. Moller, Mat. Fys. Medd. Dan. Vid. Selsk. 1, 10 (1961).
  17. D. Saez, Phys. Rev. D 27, 2839 (1983).
  18. H. Meyer, Gen. Rel. Grav. 14, 531 (1982).
  19. K. Hayashi and T. Shirafuji, Prog. Theor. Phys. 64, 866, 883, 1435, 2222; 65, 525 (1980).
  20. F. W. Hehl, J. Nitsch, and P. von der Heyde, in: General Relativity and Gravitation, A. Held, ed. (Plenum Press, New York, 1980).
  21. C. Pellegrini and J. Plebanski, Mat. Fys. Scr. Dan. Vid. Selsk. 2, no. 3 (1963).
  22. K. Hayashi and T. Nakano, Prog. Theor. Phys. 38, 491 (1967).
  23. K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).
  24. W. Kopzynski, J. Phys. A 15, 493 (1982).
  25. J. M. Nester, Class. Quantum Grav. 5, 1003 (1988).
  26. T. Kawai and N. Toma, Prog. Theor. Phys. 87, 583 (1992).
  27. V. C. de Andrade and J. G. Pereira, Phys. Rev. D 56, 4689 (1997).
  28. V. C. de Andrade, L. C. T. Guillen, and J.G. Pereira, Phys. Rev. Lett. 84, 4533 (2000); Phys. Rev. D 64, 027502 (2001).
  29. H. P. Robertson, Ann. of Math. (Princeton) 33, 496 (1932).
  30. J. P. S. Lemos, F. S. N. Lobo and S. Q. de Oliveira, Phys. Rev. D 68, 064004 (2003).
  31. N. R. Khusnutdinov, Phys. Rev. D 67, 124020 (2003).
  32. M. I. Wanas, Int. J. Theor. Phys. 24, 639 (1985).
  33. C. Moller, Ann. of Phys. 4, 347 (1958); 12, 118 (1961).
  34. F. I. Mikhail, M. I. Wanas, A. Hindawi, and E.I. Lashin, Int. J. Theor. Phys. 32, 1627 (1993).
  35. T. Shirafuji, G. G. L. Nashed, and K. Hayashi, Prog. Theor. Phys. 95, 665 (1996).
  36. G. G. L. Nashed, Nouvo Cim. B 117, 521 (2002).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page