International Journal of Theoretical Physics

, Volume 54, Issue 10, pp 3490–3499 | Cite as

Total Conserved Charges of Kerr Spacetime with One Rotation Parameter in 5-Dimensions Using Poincaré Gauge Theory

  • Gamal G. L. Nashed


A pentad field, which creates Kerr spacetime, with one rotation parameter in 5-dimensions is provided. We calculate the total conserved charges of this pentad using the approach of “invariant conserved currents”. Regularized expression through relocalization is used to get the known form of conserved charges of Kerr 5-dimensions spacetime. In contrast, the covariant calculation of conserved charge led to non-convergent results.


Kerr AdS spacetimes Total conserved charges Poincaré gauge version 



This work is partially supported by the Egyptian Ministry of Scientific Research under project No. 24-2-12.


  1. 1.
    Gibbons, G.W., Perry, M.J., Pope, C.N.: Class. Quant. Grav. 22, 1503 (2005)MATHMathSciNetCrossRefADSGoogle Scholar
  2. 2.
    Talshir, I.: Phys. Rev. D 88, 024050 (2013)CrossRefADSGoogle Scholar
  3. 3.
    Fischetti, S., Kelly, W., Marolf, D.: The springer handbook of spacetime, edited by Ashtekar, A. Petkov. V. (Springer-Verlag) (2014)Google Scholar
  4. 4.
    Obukhov, Y.N., Rubilar, G.F.: Phys. Rev. D 76, 124030 (2007)MathSciNetCrossRefADSGoogle Scholar
  5. 5.
    Obukhov, Y.N., Rubilar, G.F.: Phys. Lett B660, 240 (2008)MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    Landau, L.D., Lifshitz, E. M.: The Classical Theory of Fields. Pergamon Press, Oxford (1980)Google Scholar
  7. 7.
    Szabados, L.B.: Class. Quant. Grav. 9, 2521 (1992)MATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Møller, C.: Tetrad Fields and Conservation Laws in General Relativity, Proceedings of the International School of Physics “Enrico Fermi”, edited by C. Møller (Academic Press, London, 1962); Conservation Laws in the Tetrad Theory of Gravitation, Proceedings of the Conference on Theory of Gravitation, Warszawa and Jablonna 1962 (Gauthier-Villars, Paris, and PWN-Polish Scientific Publishers, Warszawa, 1964) (NORDITA Publications No. 136)Google Scholar
  9. 9.
    Pellegrini, C., Plebański, J.: Mat. Fys. Scr. Dan. Vid. Selsk. 2(4) (1963)Google Scholar
  10. 10.
    Mikhail, F.I., Wanas, M.I., Lashin, E.I., Hindawi, A.: Gen. Rel. Grav. 26, 869 (1994)MATHMathSciNetCrossRefADSGoogle Scholar
  11. 11.
    Wanas, M.I., Youssef, N.L., Sid-Ahmed, A.M.: Class. Quant. Grav. 27, 045005 (2010)MathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Hehl, F.W.: In proceedings of the 6th school of cosmology and gravitation on spin, torsion, rotation and supergravity Erice, 1979. In: Bergmann, P.G., de Sabbata, V. (eds.) . Plenum, New York (1980)Google Scholar
  13. 13.
    Hehl, F.W., McCrea, J.D., Mielke, E.W., Neeman, Y.: Phys. Rep. 258(1) (1995)Google Scholar
  14. 14.
    Hayashi, K.: Phys. Lett. 69B, 441 (1977)CrossRefADSGoogle Scholar
  15. 15.
    Hayashi, K., Shirafuji, T.: Phys. Rev. D19, 3524 (1979). Phys. Rev. D24, 3312 (1981)MathSciNetADSGoogle Scholar
  16. 16.
    Blagojević, M., Vasilić, M.: Class. Quant. Grav. 5, 1241 (1988)MATHCrossRefADSGoogle Scholar
  17. 17.
    Kawai, T.: Phys. Rev. D62, 104014 (2000). T. Kawai, K. Shibata and I. Tanaka, Prog. Theor. Phys. 104 (2000) 505.ADSGoogle Scholar
  18. 18.
    Cho, Y. M.: Phys. Rev. D14, 2521 (1976)Google Scholar
  19. 19.
    Gronwald, F.: Int. J. Mod. Phys. D6, 263 (1997)MathSciNetCrossRefADSGoogle Scholar
  20. 20.
    Muench, U.: Über teleparallele Gravitationstheorien. Diploma Thesis, University of Cologne (1997)Google Scholar
  21. 21.
    de Andrade, V.C., Pereira, J.G.: Phys. Rev D56, 4689 (1997)MathSciNetADSGoogle Scholar
  22. 22.
    Tresguerres, R.: Int. J. Geom. Meth. Mod. Phys. 5, 905 (2008)MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Obukhov, Y.N., Pereira, J.G.: Phys. Rev. D67, 044016 (2003)MathSciNetADSGoogle Scholar
  24. 24.
    Obukhov, Y.N., Pereira, J.G.: Phys. Rev. D69, 128502 (2004)ADSGoogle Scholar
  25. 25.
    Puetzfeld, D.: An exact-plane fronted wave solution in metric-affine gravity, In: Exact solu- tions and scalar field in gravity: Recent Developments, Macías, A. Cervantes-Cota, J. Lämmerzahl, C. (Kluwer, Dordrecht, 2001)Google Scholar
  26. 26.
    García, A., Macías, A., Puetzfeld, D., Socorro, J.: Phys. Rev. D62, 044021 (2000)ADSGoogle Scholar
  27. 27.
    King, A.D., Vassiliev, D.: Class. Quant. Grav. 18, 2317 (2001)MATHMathSciNetCrossRefADSGoogle Scholar
  28. 28.
    Pasic, V., Vassiliev, D.: Class. Quant. Grav. 22, 3961 (2005)MATHMathSciNetCrossRefADSGoogle Scholar
  29. 29.
    Vassiliev, D.: Gen. Rel. Grav 34, 1239 (2002)MATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Vassiliev, D.: Ann. Phys. (Leipzig) 14, 231 (2005)MATHMathSciNetCrossRefADSGoogle Scholar
  31. 31.
    Obukhov, Y.N.: Phys. Rev. D 73, 024025 (2006)MathSciNetCrossRefADSGoogle Scholar
  32. 32.
    Obukhov, Y.N., Rubilar, G.F., Pereira, J.G.: Phys. Rev. D74, 104007 (2006)MathSciNetADSGoogle Scholar
  33. 33.
    Obukhov, Y.N., Rubilar, G.F.: Phys. Rev. D73, 124017 (2006)MathSciNetADSGoogle Scholar
  34. 34.
    Hehl, F.W., McCrea, J.D., Mielke, E.W., Néeman, Y.: Phys. Rep 258, 1 (1995)MathSciNetCrossRefADSGoogle Scholar
  35. 35.
    Blagojević, M., Vasilić, M.: Class. Quant. Grav. 5, 1241 (1988)MATHCrossRefADSGoogle Scholar
  36. 36.
    Nashed, G.G.L.: Eur. Phys. J. C 54, 291 (2008)MATHMathSciNetCrossRefADSGoogle Scholar
  37. 37.
    Hehl, F.W., Né eman, Y., Nitsch, J., Von der Heyde, P.: Phys. Lett. B78, 102 (1978)CrossRefADSGoogle Scholar
  38. 38.
    Aldrovandi, R., Guillen, L.C.T., Pereira, J.G., Vu, K.H.: Bringing Together Gravity and the Quanta.” Contribution to the Proceedings of the Albert Einstein Century International Conference, Paris, July 1822. arXiv:gr-qc/0603122(2005)
  39. 39.
    Nashed, G.G.L.: Ann. Phys. (Berlin) 523, 450 (2011)MathSciNetCrossRefADSGoogle Scholar
  40. 40.
    Aldrovandi, R., Lucas, T.G., Pereira, J.G.: Gravitational Energy-Momentum Conservation in Teleparallel Gravity. arXiv:0812.0034
  41. 41.
    Lucas, T.G., Obukhov, Y.N., Pereira, J.G.: Phys. Rev. D 80, 064043 (2009)CrossRefADSGoogle Scholar
  42. 42.
    Obukhov, Y., Rubilar, G.F.: Phys. Rev. D 74, 064002 (2006)MathSciNetCrossRefADSGoogle Scholar
  43. 43.
    Komar, A.: Phys. Rev. 127, 1411 (1962)MATHMathSciNetCrossRefADSGoogle Scholar
  44. 44.
    Szabados, L.B.: Quasi-local energy-momentum and angular momentum in GR: A review article, Living. Rev. Rel. 7, 4 (2004) []Google Scholar
  45. 45.
    Nashed, G.G.L., Phys, Mod.: Lett. A 22, 1047 (2007)MATHGoogle Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsThe British University in EgyptSherouk CityEgypt
  2. 2.Mathematics Department, Faculty of ScienceAin Shams UniversityCairoEgypt

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