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Extended Birkhoff’s theorem in f(T) gravity

  • Regular Article - Theoretical Physics
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Abstract

f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, Eur. Phys. J. (2011), arXiv:1107.0629v1], we prove that Birkhoff’s theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss, respectively, the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of Birkhoff’s theorem in the frame of f(T) gravity via a conformal transformation by regarding the Brans–Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.

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References

  1. R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  2. G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009)

    Article  ADS  Google Scholar 

  3. E.V. Linder, Phys. Rev. D 81, 127301 (2010)

    Article  ADS  Google Scholar 

  4. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928)

  5. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 224 (1928)

  6. R. Aldrovandi, J.G. Pereira, An Introduction to Teleparallel Gravity (Instituto de Fisica Teorica, UNSEP, Sao Paulo, 2007) (http://www.ift.unesp.br/gcg/tele.pdf)

    Google Scholar 

  7. J. Garechi (2010), arXiv:1010.2654

  8. S. Nojiri, S.D. Odintsov, Gen. Relativ. Gravit. 36, 1765–1780 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  9. S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59–144 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  10. S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Li et al., Commun. Theor. Phys. 56, 525–604 (2011)

    Article  ADS  Google Scholar 

  12. X.H. Meng, P. Wang, Class. Quantum Gravity 20, 4949 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. X.H. Meng, P. Wang, Class. Quantum Gravity 21, 951 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. X.H. Meng, P. Wang, Class. Quantum Gravity 21, 2029 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  15. X.H. Meng, P. Wang, Class. Quantum Gravity 22, 23 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  16. X.H. Meng, P. Wang, Gen. Relativ. Gravit. 36, 1947 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. X.H. Meng, P. Wang, Phys. Lett. B 584, 1 (2004)

    Article  ADS  Google Scholar 

  18. P. Wang, X.H. Meng, Class. Quantum Gravity 22, 283 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  19. J. Ren, X.H. Meng, Phys. Lett. B 633, 1 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Ren, X.H. Meng, Phys. Lett. B 636, 5 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  21. M.G. Hu, X.H. Meng, Phys. Lett. B 635, 186 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  22. J. Ren, X.H. Meng, Int. J. Mod. Phys. D 16, 1341 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. E. Flanagan, Class. Quantum Gravity 21, 417 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  24. S. Nojiri, S. Odintsov, Phys. Lett. B 576, 5 (2003)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  25. S. Nojiri, S. Odintsov, Phys. Rev. D 68, 123512 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Volink, Phys. Rev. D 68, 063510 (2003)

    Article  ADS  Google Scholar 

  27. S. Capozziello, M. Francaviglia, Gen. Relativ. Gravit. 40, 357 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. T. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451–497 (2010)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  29. A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010)

    ADS  Google Scholar 

  30. B.J. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 064035 (2011)

    Article  ADS  Google Scholar 

  31. R.J. Yang, Eur. Phys. Lett. 93, 60001 (2011)

    Article  ADS  Google Scholar 

  32. K. Bamba et al., J. Cosmol. Astropart. Phys. 1101, 021 (2011)

    Article  ADS  Google Scholar 

  33. K. Bamba et al. (2010), arXiv:1008.4036

  34. P. Wu, H. Yu, Phys. Lett. B 693, 415–420 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  35. R. Myrzakulov (2010), arXiv:1006.1120

  36. K.K. Yerzhanov et al. (2010), arXiv:1006.3879

  37. R.J. Yang, Eur. Phys. J. C 71, 1797 (2011)

    Article  ADS  Google Scholar 

  38. G.R. Bengochea, Phys. Lett. B 695, 405–411 (2011)

    Article  ADS  Google Scholar 

  39. M. Hamani Daouda et al., Eur. Phys. J. C 71, 1817 (2011)

    Article  ADS  Google Scholar 

  40. M. Hamani Daouda et al., Eur. Phys. J. C 72, 1890 (2012)

    Article  ADS  Google Scholar 

  41. X.-h. Meng, Y.-b. Wang, Europhys. Lett. 71, 1755 (2011)

    Google Scholar 

  42. G.D. Birkhoff, Relativity and Modern Physics (Harvard University Press, Cambridge, 1923)

    MATH  Google Scholar 

  43. S. Deser, J. Franklin, Am. J. Phys. 73, 261 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. N.V. Johansen, F. Ravndal, Gen. Relativ. Gravit. 38, 537 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. S. Deser, Gen. Relativ. Gravit. 37, 2251 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  46. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972)

    Google Scholar 

  47. C.G. Böhmer, A. Mussa, N. Tamanini (2011), arXiv:1107.4455v2

  48. Y. Liu, S.N. Zhang, Phys. Lett. B 679, 88–94 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  49. R.F. Penna, Phys. Lett. B 707, 233–236 (2012)

    Article  ADS  Google Scholar 

  50. S.W. Hawking, Commun. Math. Phys. 25, 167 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  51. S.W. Hawking, Commun. Math. Phys. 25, 152 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  52. S. Capozziello, A. Stabile, A. Troisi, Phys. Rev. D 76, 104019 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  53. V. Faraoni, Phys. Rev. D 81, 044002 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  54. S. Capozziello, D. Sáez-Gómez (2011), arXiv:1107.0948

  55. S.H. Chen et al., Phys. Rev. D 83, 023508 (2011)

    Article  ADS  Google Scholar 

  56. J.B. Dent, S. Dutta, E.N. Saridakis, J. Cosmol. Astropart. Phys. 1101, 009 (2011)

    Article  ADS  Google Scholar 

  57. Y.-F. Cai et al., Class. Quantum Gravity 28, 215011 (2011)

    Article  ADS  Google Scholar 

  58. H. Dong, Y.-b. Wang, X.-h. Meng, The validity of Birkhoff’s theorem in the f(T) gravity using a perturbative approach

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Acknowledgements

We cordially thank Prof. Lewis H. Ryder and Prof. Sergei D. Odintsov for lots of interesting discussions on possible roles the torsion may play in gravity and cosmology physics during the project over years. This work is partly supported by Natural Science Foundation of China under Grant Nos. 11075078 and 10675062 and by the project of knowledge Innovation Program (PKIP) of Chinese Academy of Sciences (CAS) under the grant No. KJCX2.YW.W10 through the KITPC where we have initiated this present work.

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Authors and Affiliations

  1. Department of Physics, Nankai University, Tianjin, 300071, China

    Han Dong, Ying-bin Wang & Xin-he Meng

  2. Kavli Institute of Theoretical Physics China, CAS, Beijing, 100190, China

    Xin-he Meng

Authors
  1. Han Dong
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  2. Ying-bin Wang
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  3. Xin-he Meng
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Correspondence to Han Dong.

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Dong, H., Wang, Yb. & Meng, Xh. Extended Birkhoff’s theorem in f(T) gravity. Eur. Phys. J. C 72, 2002 (2012). https://doi.org/10.1140/epjc/s10052-012-2002-5

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  • DOI: https://doi.org/10.1140/epjc/s10052-012-2002-5

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