Skip to main content
SpringerLink
Log in

Static spherically symmetric solutions in F(R) gravity

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

Abstract

A Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits one to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in F(R)-gravity. All known exact solutions are recovered. We also exhibit a new non-trivial solution with non-constant Ricci scalar.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007). arXiv:hep-th/0601213

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Nojiri, S.D. Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models. arXiv:1011.0544 [gr-qc]

  3. T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, S. Zerbini, J. Cosmol. Astropart. Phys. 0502, 010 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  5. G. Cognola, S. Zerbini, J. Phys. A 39, 6245 (2006). arXiv:hep-th/0511233

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. G. Cognola, L. Sebastiani, S. Zerbini, in Proceedings MG12, arXiv:1006.1586 [gr-qc] (2009, to appear)

  7. V. Faraoni, Phys. Rev. D 74, 104017 (2006). arXiv:astro-ph/0610734

    Article  MathSciNet  ADS  Google Scholar 

  8. G. Cognola, M. Gastaldi, S. Zerbini, Int. J. Theor. Phys. 47, 898 (2008). arXiv:gr-qc/0701138

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Hu, I. Sawicki, Phys. Rev. D 76, 064004 (2007). arXiv:0705.1158 [astro-ph]

    Article  ADS  Google Scholar 

  10. E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion. arXiv:1012.2280 [hep-th] (2010)

  11. G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 77, 046009 (2008). arXiv:0712.4017 [hep-th]

    Article  ADS  Google Scholar 

  12. G. Cognola, E. Elizalde, L. Sebastiani, S. Zerbini, Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity. arXiv:1007.4676 [hep-th] (2010)

  13. S. Nojiri, S.D. Odintsov, Phys. Lett. B 657, 238 (2007). arXiv:0707.1941 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  14. S. Nojiri, S.D. Odintsov, Phys. Rev. D 77, 026007 (2008). arXiv:0710.1738 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  16. T. Multamaki, I. Vilja, Phys. Rev. D 74, 064022 (2006)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 25, 085004 (2008). arXiv:0709.0891 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  19. T.R.P. Carames, E.R. Bezerra de Mello, Eur. Phys. J. C 64, 113–121 (2009). arXiv:0901.0814 [gr-qc]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. R. Saffari, S. Rahvar, Phys. Rev. D 77, 104028 (2008)

    Article  ADS  Google Scholar 

  21. R. Saffari, S. Rahvar, Mod. Phys. Lett. A 24, 305–309 (2009)

    Article  ADS  MATH  Google Scholar 

  22. A. Vilenkin, Phys. Rev. D 32, 2511 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  23. S. Capozziello, Int. J. Mod. Phys. D 11, 4483 (2002)

    Article  Google Scholar 

  24. M.K. Parikh, F. Wilczek, Phys. Rev. Lett. 85, 5042 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  25. M. Angheben, M. Nadalini, L. Vanzo, S. Zerbini, J. High Energy Phys. 0505, 014 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  26. M. Nadalini, L. Vanzo, S. Zerbini, J. Phys. A, Math. Gen. 39, 6601 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. E. Bellini, R. Di Criscienzo, L. Sebastiani, S. Zerbini, Entropy 12, 2186 (2010). arXiv:1009.4816 [gr-qc]

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini, G. Zoccatelli, Phys. Lett. B 657, 107 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  29. S.A. Hayward, R. Di Criscienzo, L. Vanzo, M. Nadalini, S. Zerbini, Class. Quantum Gravity 26, 062001 (2009)

    Article  ADS  Google Scholar 

  30. R. Di Criscienzo, S.A. Hayward, M. Nadalini, L. Vanzo, S. Zerbini, Class. Quantum Gravity 27, 015006 (2010)

    Article  ADS  Google Scholar 

  31. R.M. Wald, Phys. Rev. D 48, 3427 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  32. M. Visser, Phys. Rev. D 48, 5697 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  33. V. Faraoni, Entropy 12, 1246 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  34. S. Deser, B. Tekin, Phys. Rev. D 75, 084032 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  35. Y. Gong, A. Wong, Phys. Rev. Lett. 99, 211301 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  36. G. Abreu, M. Visser, Phys. Rev. Lett. 105, 041302 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  37. R.G. Cai, L.M. Cao, Y.P. Hu, N. Ohta, Phys. Rev. D 80, 104016 (2009). arXiv:0910.2387 [hep-th]

    Article  ADS  Google Scholar 

  38. S. Nojiri, S.D. Odintsov, H. Stefancic, Phys. Rev. D 74, 086009 (2006). arXiv:hep-th/0608168

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Trento, Trento, Italy

    L. Sebastiani & S. Zerbini

  2. Gruppo Collegato di Trento, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italy

    L. Sebastiani & S. Zerbini

Authors
  1. L. Sebastiani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Zerbini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Sebastiani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sebastiani, L., Zerbini, S. Static spherically symmetric solutions in F(R) gravity. Eur. Phys. J. C 71, 1591 (2011). https://doi.org/10.1140/epjc/s10052-011-1591-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjc/s10052-011-1591-8

Keywords

Search

Navigation