Skip to main content
Log in

New astrophysical aspects from Yukawa fractional potential correction to the gravitational potential in D dimensions

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

The aim of this paper is to generalize in D = d + 1 the Newtonian gravity by adding to the gravitational potential for fractal distribution of particles within the linearized theory, a propagating fractional correctional mode which have the form of Yukawa (exponential) fractional potential. Exact solutions of Einstein field equations are presented where many interested features are derived and discussed in some details.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K B Oldham and J Spanier The Fractional Calculus (New York: Academic Press) (1974)

    MATH  Google Scholar 

  2. S Samko, A Kilbas and O Marichev Fractional Integrals and derivatives: Theory and Applications (New York: Gordon and Breach) (1993)

    MATH  Google Scholar 

  3. K S Miller and B Ross An Introduction to the Fractional Calculus and Fractional Differential Equations ( New York: Wiley) (1993)

    MATH  Google Scholar 

  4. I Podlubny An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of Their Applications (New York: Academic Press) (1999)

    MATH  Google Scholar 

  5. R Hilfer Applications of Fractional Calculus in Physics (New Jersey: Word Scientific Publishing Co.) (2000)

  6. M K Kolwankar arXiv:chao-dyn/9811008v1 (1998)

  7. N Roy Mon. Not. Roy. Astron. Soc. 378 L34 (2007)

    Article  ADS  Google Scholar 

  8. N Roy and A K Ray Mon. Not. Roy. Astron. Soc. 380 733 (2007)

    Article  ADS  Google Scholar 

  9. N Roy and A K Ray Mon. Not. Roy. Astron. Soc. 397 1374 (2009)

    Article  ADS  Google Scholar 

  10. A Jahan and D K Choudhury Indian J. Phys. 85 587 (2011)

    Article  ADS  Google Scholar 

  11. V E Tarasov Celest. Mech. Dyn. Syst. 94 1 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. A Provenzale Fractals and the Large-Scale Galaxy Distribution, Lectures Notes in Physics Monographs: Applying Fractals in Astronomy, vol 3 (Berlin: Springer) p 97 (1991)

  13. V E Tarasov Ann. Phys. 318 286 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. A Connes Noncommutative Geometry (London: Academic Press) (1994)

    MATH  Google Scholar 

  15. O Lauscher and M Reuter JHEP 10 050 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  16. G E Brown and A D Jackson The Nucleon–Nucleon Interaction (Amsterdam: North-Holland Publishing, ISBN 0-7204-0335-9) (1976).

  17. C M Will Theory and Experiments in Gravitational Physics (Cambridge: Cambridge University Press) (1993)

    Book  Google Scholar 

  18. S Capoziello et al Mod. Phys. Lett. A16 693 (2001)

    ADS  Google Scholar 

  19. J D Anderson et al Phys. Rev. Lett. 81 2858 (1998)

    Article  ADS  Google Scholar 

  20. R H Sanders Ann. Rev. Astron. Astrophys. 2 1 (1990)

    Article  Google Scholar 

  21. O Aursjø Microscopic Black Holes and Extra Dimensions, Candidatus Scientiarum Thesis (Department of Physics, University of Oslo) (2005)

  22. S Weinberg Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York: Wiley) p 657 (1979).

  23. S Ray, F Rahaman and U Mukhopadhyay Int. J. Mod. Phys. D18 781 (2009)

    ADS  Google Scholar 

  24. M P Dabrowski and J Stelmach Astron. J. 97 978 (1989)

    Article  ADS  Google Scholar 

  25. S E Rugh Chaos in the Einstein equations-characterization and importance in Deterministic Chaos in General Relativity (eds.) D Hobill, A Burd and A Coley (New York: Plenum) (1994)

  26. L Bombelli and E Calzetta Class. Quantum Gravity 9 2573 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  27. N J Cornish and N E Franke Phys. Rev. D56 1903 (1997)

    ADS  Google Scholar 

  28. E N Glass and J P Krisch Class. Quantum Gravity. 17 2611 (2000)

    Article  MATH  Google Scholar 

  29. A Nandi, S Manickam and S K Chakrabarti Indian J. Phys. 74B 331 (2000)

    Google Scholar 

  30. S K Chakrabarti, S K Mandal, S Sasmal, D Bhowmick, A K Choudhurya and N N Patra Indian J. Phys. 84 1461 (2010)

    Article  ADS  Google Scholar 

  31. P Das and A Deshmukhya Indian J. Phys. 84 617 (2010)

    Article  Google Scholar 

  32. S Ray, S K Chakrabarti and S Sasmal Indian J. Phys. 86 85 (2012)

    Google Scholar 

  33. S K Chakrabarti et al Indian J. Phys. 86 323 (2012)

  34. A Jain, S Tiwari, S Jain and A K Gwal Indian J. Phys. 85 1367 (2011)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ahmad Rami El-Nabulsi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

El-Nabulsi, A.R. New astrophysical aspects from Yukawa fractional potential correction to the gravitational potential in D dimensions. Indian J Phys 86, 763–768 (2012). https://doi.org/10.1007/s12648-012-0143-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-012-0143-x

Keywords

PACS Nos.

Navigation