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Quantum singularities in a model of f(R) gravity

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Abstract

The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein–Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r=0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity remains quantum mechanically singular when it is probed with quantum fields having different spin structures.

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References

  1. S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  2. T. Clifton, J.D. Barrow, Phys. Rev. D 72, 103005 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  3. T. Multamaki, I. Vilja, Phys. Rev. D 76, 064021 (2007)

    Article  ADS  Google Scholar 

  4. M.D. Seifert, Phys. Rev. D 76, 064002 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  5. L. Hollenstein, F.S.N. Lobo, Phys. Rev. D 78, 124007 (2008)

    Article  ADS  Google Scholar 

  6. A. de la Cruz-Dombriz, A. Dobado, A.L. Maroto, Phys. Rev. D 80, 124011 (2009)

    Article  ADS  Google Scholar 

  7. S. Habib Mazharimousavi, M. Halilsoy, T. Tahamtan, Eur. Phys. J. C 72, 1851 (2012)

    Article  ADS  Google Scholar 

  8. M. Barriola, A. Vilenkin, Phys. Rev. Lett. 63, 341 (1989)

    Article  ADS  Google Scholar 

  9. P.S. Letelier, Phys. Rev. D 20, 1294 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  10. S. Capozziello, M. De Laurentis, Phys. Rep. 509, 167 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  11. R.M. Wald, J. Math. Phys. (N.Y.) 21, 2082 (1980)

    Google Scholar 

  12. G.T. Horowitz, D. Marolf, Phys. Rev. D 52, 5670 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Ishibashi, A. Hosoya, Phys. Rev. D 60, 104028 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  14. D.A. Konkowski, T.M. Helliwell, Gen. Relativ. Gravit. 33, 1131 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. T.M. Helliwell, D.A. Konkowski, V. Arndt, Gen. Relativ. Gravit. 35, 79 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. D.A. Konkowski, T.M. Helliwell, C. Wieland, Class. Quantum Gravity 21, 265 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. D.A. Konkowski, C. Reese, T.M. Helliwell, C. Wieland, Classical and quantum singularities of Levi-Civita spacetimes with and without a cosmological constant, in Proceedings of the Workshop on the Dynamics and Thermodynamics of Black Holes and Naked Singularities, ed. by L. Fatibene, M. Francaviglia, R. Giambo, G. Megli (2004)

    Google Scholar 

  18. D.A. Konkowski, T.M. Helliwell, Int. J. Mod. Phys. A 26(22), 3878–3888 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  19. J.P.M. Pitelli, P.S. Letelier, J. Math. Phys. 48, 092501 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  20. J.P.M. Pitelli, P.S. Letelier, Phys. Rev. D 77, 124030 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  21. J.P.M. Pitelli, P.S. Letelier, Phys. Rev. D 80, 104035 (2009)

    Article  ADS  Google Scholar 

  22. P.S. Letelier, J.P.M. Pitelli, Phys. Rev. D 82, 104046 (2010)

    Article  ADS  Google Scholar 

  23. O. Unver, O. Gurtug, Phys. Rev. D 82, 084016 (2010)

    Article  ADS  Google Scholar 

  24. S. Habib Mazharimousavi, O. Gurtug, M. Halilsoy, Int. J. Mod. Phys. D 18, 2061–2082 (2009)

    Article  ADS  MATH  Google Scholar 

  25. S. Habib Mazharimousavi, M. Halilsoy, I. Sakalli, O. Gurtug, Class. Quantum Gravity 27, 105005 (2010)

    Article  ADS  Google Scholar 

  26. S. Habib Mazharimousavi, O. Gurtug, M. Halilsoy, O. Unver, Phys. Rev. D 84, 124021 (2011)

    Article  ADS  Google Scholar 

  27. M. Reed, B. Simon, Functional Analysis (Academic Press, New York, 1980)

    MATH  Google Scholar 

  28. M. Reed, B. Simon, Fourier Analysis and Self-adjointness (Academic Press, New York, 1975)

    Google Scholar 

  29. R.D. Richtmyer, Principles of Advanced Mathematical Physics (Springer, New York, 1978)

    Book  MATH  Google Scholar 

  30. S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, London, 1992)

    Google Scholar 

  31. I. Seggev, Class. Quantum Gravity 21, 2651 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Eastern Mediterranean University, G. Magusa, north Cyprus, Mersin 10, Turkey

    O. Gurtug & T. Tahamtan

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  1. O. Gurtug
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  2. T. Tahamtan
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Correspondence to O. Gurtug.

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Gurtug, O., Tahamtan, T. Quantum singularities in a model of f(R) gravity. Eur. Phys. J. C 72, 2091 (2012). https://doi.org/10.1140/epjc/s10052-012-2091-1

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  • DOI: https://doi.org/10.1140/epjc/s10052-012-2091-1

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