Wormhole Solution and Energy in Teleparallel Theory of Gravity

• Authors: G. Nashed
• Languages of publication: EN

Abstracts

EN

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two parameters k_1, k_2 of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation ρ= ρ_t=0 with ρ=T_{i,j}u^iu^j, ρ_t =(T_{ij}-1/2Tg_{ij}) u^iu^j, where u^iu_i=-1. From this solution which contains an arbitrary function we can generate the other two solutions obtained before. The associated metric of this space-time is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculating the energy content of this tetrad field and using the gravitational energy momentum given by Møller in the teleparallel space-time we find that the resulting form depends on the arbitrary function and does not depend on the two parameters k_1 and k_2 characterizing the wormhole. Using the regularized expression of the gravitational energy momentum we get the value of energy which does not depend on the arbitrary function.

Keywords

EN

04.20.Cv; 04.50.+h; 04.20.-q

Discipline

• 04.20.Cv: Fundamental problems and general formalism
• 04.20.-q: Classical general relativity(see also 02.40.-k Geometry, differential geometry, and topology)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2007
• Volume: 111
• Issue: 2
• Pages: 201-213

Dates

published

2007-02

received

2006-12-10

Contributors

author

G. Nashed

• Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt, Cairo, Egypt

References

• 1. Y. Itin, Class. Quant. Grav., 19, 173, 2002
• 2. Y. Itin, J. Math. Phys., 46, 012501, 2005
• 3. F.W. Hehl, Y. Neeman, J. Nitsch, P. Von der Heyde, Phys. Lett. B, 78, 102, 1978
• 4. F.W. Hehl, in: Spin, Torsion and Supergravity, Eds. P.G. Bergmann, V. De Sabbata, Plenum, New York 1980, p. 5
• 5. T. Kawai, Phys. Rev. D, 49, 2862, 1994; Phys. Rev. D, 62, 104014, 2000
• 6. M. Blagojević, M. Vasilić, Class. Quant. Grav., 17, 3785, 2000
• 7. M. Blagojević, I.A. Nikolić, Phys. Rev. D, 62, 024021, 2000
• 8. F.W. Hehl, J.D. MacCrea, E.W. Mielke, Y. Neéman, Phys. Rep., 258, 1, 1995
• 9. K. Hayashi, T. Shirafuji, Phys. Rev. D, 19, 3524, 1979
• 10. J. Nitsch, F.W. Hehl, Phys. Lett. B, 90, 98, 1980
• 11. E.W. Mielke, Phys. Rev. D, 42, 3388, 1990
• 12. R.S. Tung, J.M. Nester, Phys. Rev. D, 60, 021501, 1999
• 13. M. Leclerc, Phys. Rev. D, 71, 027503, 2005
• 14. E.W. Mielke, Phys. Rev. D, 69, 128501, 2004
• 15. Yu.N. Obukhov, J.G. Pereira, Phys. Rev. D, 69, 128502, 2004
• 16. Yu.N. Obukhov, J.G. Pereira, Phys. Rev. D, 67, 044016, 2003
• 17. J.W. Maluf, J. Math. Phys., 35, 335, 1994
• 18. J.W. Maluf, J.F. da Rocha-neto, T.M.L. Toribio, K.H. Castello-Branco, Phys. Rev. D, 65, 124001, 2002
• 19. C. Moller, Ann. Phys., 12, 118, 1961
• 20. C. Moller, Mat. Fys. Medd. Dan. Vid. Selsk., 1, 10, 1961
• 21. C. Moller, Nucl. Phys., 57, 330, 1964
• 22. C. Moller, Mat. Fys. Medd. Dan. Vid. Selsk., 39, 13, 1978
• 23. L. Flamm, Phys. Z., 17, 48, 1916
• 24. M.S. Morris, K.S. Thorne, Am. J. Phys., 56, 395, 1988
• 25. M. Visser, Lorentzian Wormholes -- From Einstein to Hawking, American Institute of Physics, New York 1996
• 26. P.K.F. Kuhfittig, Phys. Rev. D, 67, 064015, 2003
• 27. T.A. Roman, Phys. Rev. D, 47, 1370, 1993
• 28. M.S. Morris, K.S. Thorne, U. Yurtsever, Phys. Rev. Lett., 61, 1446, 1988
• 29. H. Epstein, E. Glaser, A. Yaffe, Nuovo Cimento, 36, 2296, 1965
• 30. M. Visser, D. Hochberg, gr-qc/9710001
• 31. D. Hochberg, Phys. Lett. B, 251, 349, 1990; B. Bhawal, S. Kar, Phys. Rev. D, 46, 2464, 1992
• 32. S. Kar, Phys. Rev. D, 49, 862, 1994; S. Kar, D. Sahdev, Phys. Rev. D, 53, 722, 1996
• 33. D. Hochberg, M. Visser, Phys. Lett., 81, 764, 1998; Phys. Rev. D, 58, 044021, 1998
• 34. N. Dadhich, S. Kar, S. Mukherjee, M. Visser, Phys. Rev. D, 65, 064004, 2002
• 35. D. Hochberg, M. Visser, gr-qc/9901020
• 36. H.P. Robertson, Ann. Math. (Princeton), 33, 496, 1932
• 37. K. Hayashi, T. Nakano, Prog. Theor. Phys., 38, 491, 1967
• 38. G.G.L. Nashed, submitted to Nuovo Cimento B
• 39. C. Moller, Ann. Phys., 4, 347, 58; 12, 118, 1961
• 40. F.I. Mikhail, M.I. Wanas, A. Hindawi, E.I. Lashin, Int. J. Theor. Phys., 32, 1627, 1993
• 41. T. Shirafuji, G.G.L. Nashed, K. Hayashi, Prog. Theor. Phys., 95, 665, 1996
• 42. J.D. Brown, J.W. York, Jr., in: Proc. Joint Summer Research Conf. on Mathematical Aspects of Classical Field Theory, in series: Contemporary Mathematics, Vol. 132, Eds. M.J. Gotay, J.E. Marsden, V. Moncrief, American Mathematical Society, Providence (USA) 1992, p. 129; Phys. Rev. D, 47, 1407, 1993
• 43. J.W. Maluf, M.V.O. Veiga, J.F. da Rocha-neto, gr-qc/0507122
• 44. J.W. Maluf, J.F. da Rocha-neto, Phys. Rev. D, 64, 084014, 2001
• 45. G.G.L. Nashed, Gen. Rel. Grav., 34, 1047, 2002
• 46. J.P.S. Lemos, F.S.N. Lobo, S.Q. de Oliveira, Phys. Rev. D, 68, 064004, 2003

Identifiers

DOI

10.12693/APhysPolA.111.201