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Generalized parallel transport and coordinate transformations in f(R) gravity

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Abstract

In this paper, we study the generalized parallel transport of vectors and generalized coordinate transformations between generalized reference frames described in f(R) gravity. After constructing the generalized parallel transport relations and the generalized transformation laws in f(R) gravity, we discuss the implications of these laws and present the differences between f(R) gravity and Einstein’s general relativity. For a constant Ricci scalar case with de Sitter-like behavior for a de Sitter space-time, we find that the parallel transport is invariant under the conformal transformation from general relativity to f(R) gravity. However, for a non-de Sitter space-time, parallel transport differs by an extra field term.

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References

  1. R. A. Nelson, J. Math. Phys. 28, 2379 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  2. H. Nikolic, Am. J. Phys. 67, 1007 (1999).

    Article  ADS  Google Scholar 

  3. H. Nikolic, Phys. Rev. A 61, 032109, 1 (2000).

    Article  MathSciNet  Google Scholar 

  4. O. Gron, Am. J. Phys. 45, 65 (1977).

    Article  ADS  Google Scholar 

  5. O. Gron, Am. J. Phys. 43, 869 (1975).

    Article  ADS  Google Scholar 

  6. R. D’Inverno, Introtucing Einstein’s Relativity (Oxford University Press, UK, 1992).

    MATH  Google Scholar 

  7. H. A. Buchdahl, Monthly Notices Roy. Astro. Soc. 150, 1 (1970).

    Article  ADS  Google Scholar 

  8. A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).

    Article  ADS  Google Scholar 

  9. H. Kleinert et al., Gen. Relativ. Grav. 34, 1295 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Nojiri et al., Int. J. Geom. Meth. Mod. Phys. 04, 115 (2007).

    Article  MathSciNet  Google Scholar 

  11. S. Nojiri et al., Phys. Rep. 505, 59 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  12. K. Bamba et al., Astrophys. Space Sci. 342, 155 (2012).

    Article  ADS  Google Scholar 

  13. A. A. Starobinsky, JETP Lett. 86, 157 (2007).

    Article  ADS  Google Scholar 

  14. S. Capozziello et al., Class. Quant. Grav. 25, 085004 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  15. S. Capozziello et al., Phys. Rep. 509, 167 (2011).

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Sinop University, Sinop, 57000, Turkey

    Emre Dil

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  1. Emre Dil
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Correspondence to Emre Dil.

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Dil, E. Generalized parallel transport and coordinate transformations in f(R) gravity. Journal of the Korean Physical Society 69, 1733–1738 (2016). https://doi.org/10.3938/jkps.69.1733

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  • DOI: https://doi.org/10.3938/jkps.69.1733

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