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Effects of spacetime anisotropy on the galaxy rotation curves

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Abstract

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom’s MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration GM/r 2 is smaller than the critical acceleration a 0. Interestingly, the critical acceleration a 0, although varies between different galaxies, is in the order of magnitude \(cH_{0}/2\pi\sim10^{-10}~\mathrm{m\,s}^{-2}\).

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Notes

  1. The gravitational vacuum field equation given by [52] is \(g^{F\,ab}\bar{\partial}_{a}\bar{\partial}_{b} \mathcal {R}-\frac{6}{F^{2}} \mathcal{R}+2g^{F\,ab} (\nabla_{a}S_{b}+S_{a}S_{b}+\bar{\partial}_{a}\nabla S_{b} )=0\). The S a -terms can be written as \(S_{a}=\ell ^{d}P_{d~ba}^{~b}\), where ℓ d≡y d/F and \(P_{d~ba}^{~b}\) are the coefficients of the cross basis dx∧δy/F [31]. Considering that \(\mathcal{R}=R^{a}_{~ab}y^{b}=-R^{a}_{~dab}y^{d} y^{b}=F^{2}(\ell^{d} R^{~a}_{d~ab}\ell^{b})=F^{2}(g^{ab}R_{ab})=F^{2} \mathit{Ric}\) and dropping the S a -terms, one can see that Ric=0 is one of the solutions of the above equation.

  2. The symmetry of locally Minkowski space-time is different from that of Minkowski spacetime. The space length determined by the symmetry of locally Minkowski space-time is also different from the Euclidean length. So does the unit circle and its related quantity-π. Here, we denote the Finslerian π by π F , where “∧” is the “wedge product”. For more details please refer to the book of [53].

  3. The interpolation function (23) is singular at x=0, but it is easy to show that lim x→0[μ(x)/x]=1.

  4. http://www.mpia-hd.mpg.de/THINGS/Data.html [20].

  5. http://www.astro.rug.nl/~gipsy/.

References

  1. S. Weinberg, Cosmology (Oxford University Press, New York, 2008)

    MATH  Google Scholar 

  2. E. Komatsu, et al. (WMAP Collaboration), Astrophys. J. Suppl. 192, 18 (2011)

    Article  ADS  Google Scholar 

  3. N. Suzuki et al., Astrophys. J. 746, 85 (2012)

    Article  ADS  Google Scholar 

  4. B.A. Reid et al., Mon. Not. R. Astron. Soc. 404, 60 (2010)

    Article  ADS  Google Scholar 

  5. L. Perivolaropoulos, arXiv:1104.0539

  6. A. Kashlinsky, F. Atrio-Barandela, D. Kocevski, H. Ebeling, Astrophys. J. 686, L49 (2009)

    Article  ADS  Google Scholar 

  7. A. Kashlinsky, F. Atrio-Barandela, H. Ebeling, A. Edge, D. Kocevski, Astrophys. J. 712, L81 (2010)

    Article  ADS  Google Scholar 

  8. J.K. Webb et al., Phys. Rev. Lett. 107, 191101 (2011)

    Article  ADS  Google Scholar 

  9. M. Tegmark, A. de Oliveira-Costa, A. Hamilton, Phys. Rev. D 68, 123523 (2003)

    Article  ADS  Google Scholar 

  10. K. Land, J. Magueijo, Phys. Rev. Lett. 95, 071301 (2005)

    Article  ADS  Google Scholar 

  11. I. Antoniou, L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 1012, 012 (2010)

    Article  ADS  Google Scholar 

  12. E.A. Lim, Phys. Rev. D 71, 063504 (2005)

    Article  ADS  Google Scholar 

  13. S. Kanno, J. Soda, Phys. Rev. D 74, 063505 (2006)

    Article  ADS  Google Scholar 

  14. A. Arianto, F.P. Zen, B.E. Gunara, T Triyanta, S. Supardi, J. High Energy Phys. 09, 048 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  15. T.S. Koivisto, D.F. Mota, J. Cosmol. Astropart. Phys. 08, 021 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  16. S. Koh, B. Hu, J. Korean Phys. Soc. 60, 1983 (2012)

    Article  ADS  Google Scholar 

  17. M. Watanabe, S. Kanno, J. Soda, Phys. Rev. Lett. 102, 191302 (2009)

    Article  ADS  Google Scholar 

  18. J. Lee, E. Komatsu, Astrophys. J. 718, 60 (2010)

    Article  ADS  Google Scholar 

  19. V.C. Rubin, W.K. Ford, N. Thonnard, Astrophys. J. 238, 471 (1980)

    Article  ADS  Google Scholar 

  20. F. Walter, E. Brinks, W.J.G. de Blok, F. Bigiel, R.C. Kennicutt Jr., M.D. Thornley, A.K. Leroy, Astron. J. 136, 2563 (2008)

    Article  ADS  Google Scholar 

  21. K.G. Begeman, A.H. Broeils, R.H. Sanders, Mon. Not. R. Astron. Soc. 249, 523 (1991)

    ADS  Google Scholar 

  22. M. Persic, P. Salucci, F. Stel, Mon. Not. R. Astron. Soc. 281, 27 (1996)

    Article  ADS  Google Scholar 

  23. L. Chemin, W.J.G. de Blok, G.A. Mamon, Astron. J. 142, 109 (2011)

    Article  ADS  Google Scholar 

  24. M. Milgrom, Astrophys. J. 270, 365 (1983)

    Article  ADS  Google Scholar 

  25. M. Milgrom, Astrophys. J. 270, 371 (1983)

    Article  ADS  Google Scholar 

  26. P. Horava, Phys. Rev. D 79, 084008 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  27. P. Horava, J. High Energy Phys. 0903, 020 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  28. P. Horava, Phys. Rev. Lett. 102, 161301 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  29. V.F. Cardone, N. Radicella, M.L. Ruggiero, M. Capone, Mon. Not. R. Astron. Soc. 406, 1821 (2010)

    ADS  Google Scholar 

  30. V.F. Cardone, M. Capone, N. Radicella, M.L. Ruggiero, Mon. Not. R. Astron. Soc. 423, 141 (2012)

    Article  ADS  Google Scholar 

  31. D. Bao, S.S. Chern, Z. Shen, An Introduction to Riemann–Finsler Geometry. Graduate Text in Mathematics, vol. 200 (Springer, New York, 2000)

    Book  MATH  Google Scholar 

  32. H.C. Wang, J. Lond. Math. Soc. s1-22, 5 (1947)

    Article  Google Scholar 

  33. X. Li, Z. Chang, Differ. Geom. Appl. 30, 737 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  34. G.Yu. Bogoslovsky, Il Nuovo Cimento B 40, 99 (1977)

    Article  ADS  Google Scholar 

  35. G.Yu. Bogoslovsky, Il Nuovo Cimento B 40, 116 (1977)

    Article  ADS  Google Scholar 

  36. G.Yu. Bogoslovsky, Il Nuovo Cimento B 43, 377 (1978)

    Article  ADS  Google Scholar 

  37. J.R. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Phys. Rev. D 61, 027503 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  38. F. Girelli, S. Liberati, L. Sindoni, Phys. Rev. D 75, 064015 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  39. G.W. Gibbons, J. Gomis, C.N. Pope, Phys. Rev. D 76, 081701 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  40. V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  41. Z. Chang, S. Wang, Eur. Phys. J. C 72, 2165 (2012)

    Article  ADS  Google Scholar 

  42. Z. Chang, S. Wang, Eur. Phys. J. C 73, 2337 (2013)

    Article  ADS  Google Scholar 

  43. A.P. Kouretsis, M. Stathakopoulos, P.C. Stavrinos, Phys. Rev. D 79, 104011 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  44. Z. Chang, M.-H. Li, S. Wang, arXiv:1303.1596

  45. Z. Chang, S. Wang, X. Li, Eur. Phys. J. C 72, 1838 (2012)

    Article  ADS  Google Scholar 

  46. Z. Chang, M.-H. Li, X. Li, S. Wang, arXiv:1303.1593

  47. X. Li, M.-H. Li, H.-N. Lin, Z. Chang, Mon. Not. R. Astron. Soc. 428, 2939 (2013)

    Article  ADS  Google Scholar 

  48. F.A.E. Pirani, in Lectures on General Relativit, Brandeis Summer, Institute in Theoretical Physics, vol. 1 (Prentice-Hall, Englewood Cliffs, 1964), p. 459

    Google Scholar 

  49. S.F. Rutz, Comput. Phys. Commun. 115, 300 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. S.S. Chern, Sci. Rep. Nat. Tsing Hua Univ. Ser. A 5, 95 (1948)

    MathSciNet  Google Scholar 

  51. S.S. Chern, in Selected Papers, vol. II, Mathematics: Frontiers and Perspectives, ed. by V.I. Arnol’d (Springer, Heidelberg, 1989), p. 194

    Google Scholar 

  52. C. Pfeifer, M.N.R. Wohlfarth, Phys. Rev. D 85, 064009 (2012)

    Article  ADS  Google Scholar 

  53. S.S. Chern, W.H. Chen, K.S. Lam, Lectures on Differential Geometry. Series on University Mathematics, vol. 1 (World Scientific, Beijing, 2006)

    Google Scholar 

  54. G. de Vaucouleurs, Handb. Phys. 53, 311 (1959)

    ADS  Google Scholar 

  55. K.C. Freeman, Astrophys. J. 160, 811 (1972)

    Article  ADS  Google Scholar 

  56. W.J.G. de Blok, F. Walter, E. Brinks, C. Trachternach, S.-H. Oh, R.C. Kennicutt Jr., Astron. J. 136, 2648 (2008)

    Article  ADS  Google Scholar 

  57. J. Mastache, J.L. Cervantes-Cota, A. de la Macorra, Phys. Rev. D 87, 063001 (2013)

    Article  ADS  Google Scholar 

  58. V.A. Kostelecky, N. Russell, Rev. Mod. Phys. 83, 11 (2011)

    Article  ADS  Google Scholar 

  59. D. Grumiller, Phys. Rev. Lett. 105, 211303 (2010)

    Article  ADS  Google Scholar 

  60. H.-N. Lin, M.-H. Li, X. Li, Z. Chang, Mon. Not. R. Astron. Soc. 430, 450 (2013)

    Article  ADS  Google Scholar 

  61. G.W. Angus, B. Famaey, H.S. Zhao, Mon. Not. R. Astron. Soc. 371, 138 (2008)

    Article  ADS  Google Scholar 

  62. G.W. Angus, H.Y. Shan, H.S. Zhao, B. Famaey, Astrophys. J. 654, L13 (2007)

    Article  ADS  Google Scholar 

  63. I. Ferreras, M. Sakellariadou, M.F. Yusaf, Phys. Rev. Lett. 100, 031302 (2008)

    Article  ADS  Google Scholar 

  64. I. Ferreras, N.E. Mavromatos, M. Sakellariadou, M.F. Yusaf, Phys. Rev. D 80, 103506 (2009)

    Article  ADS  Google Scholar 

  65. I. Ferreras, N.E. Mavromatos, M. Sakellariadou, M.F. Yusaf, Phys. Rev. D 86, 083507 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are grateful to Y.G. Jiang for useful discussions. This work has been funded in part by the National Natural Science Fund of China under Grant No. 11075166 and No. 11147176.

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Authors and Affiliations

  1. Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, China

    Zhe Chang, Ming-Hua Li, Xin Li, Hai-Nan Lin & Sai Wang

  2. Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 100049, Beijing, China

    Zhe Chang & Xin Li

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  1. Zhe Chang
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Correspondence to Hai-Nan Lin.

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Chang, Z., Li, MH., Li, X. et al. Effects of spacetime anisotropy on the galaxy rotation curves. Eur. Phys. J. C 73, 2447 (2013). https://doi.org/10.1140/epjc/s10052-013-2447-1

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