Skip to main content
SpringerLink
Log in

(2 + 1)-Dimensional Solutions in F(R) Gravity

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Motivated by the well-known charged BTZ black holes, we look for (2 + 1)-dimensional solutions of F(R) gravity. At first we investigate some near horizon solutions and after that we obtain asymptotically Lifshitz black hole solutions. Finally, we discuss about rotating black holes with exponential form of F(R) theory.

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. Riess, A.G. et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  2. Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  3. Eling, C., Guedens, R., Jacobson, T.: Phys. Rev. Lett. 121301, 96 (2006)

    MathSciNet  Google Scholar 

  4. Elizalde, E., Silva, P. J.: Phys. Rev. D 061501, 78 (2008)

    MathSciNet  Google Scholar 

  5. Brustein, R., Hadad, M.: Phys. Rev. Lett. 101301, 103 (2009)

    MathSciNet  Google Scholar 

  6. Hendi, S.H., Eslam Panah, B., Mousavi, S.M.: Gen. Relativ. Gravit. 44, 835 (2012)

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Bamba, K., Odintsov, S.D.: JCAP 04, 024 (2008)

    Article  ADS  Google Scholar 

  9. Carroll, S.M. et al.: Phys. Rev. D 70, 043528 (2004)

    Article  ADS  Google Scholar 

  10. de la Cruz-Dombriz, A.: Phys. Rev. D 74, 087501 (2006)

    Article  ADS  Google Scholar 

  11. Fay, S., Tavakol, R., Tsujikawa, S.: Phys. Rev. D 75, 063509 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  12. Cognola, G.: Phys. Rev. D 73, 084007 (2006)

    Article  ADS  Google Scholar 

  13. Abdalla, M.C.B., Nojiri, S., Odintsov, S.D.: Class. Quantum Gravit. 22, L35 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. Briscese, F., Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 646, 105 (2007)

    Article  ADS  Google Scholar 

  15. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 78, 046006 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  16. Bamba, K., Nojiri, S., Odintsov, S.D.: JCAP 10, 045 (2008)

    Article  ADS  Google Scholar 

  17. Kobayashi, T., Maeda, K.: Phys. Rev. D 79, 024009 (2009)

    Article  ADS  Google Scholar 

  18. Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005)

    Article  ADS  Google Scholar 

  19. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  20. Boehmer, C.G., Harko, T., Lobo, F.S.N.: Astropart. Phys. 29, 386 (2008)

    Article  ADS  Google Scholar 

  21. Xue, Z., Cui, S. L. arXiv:gr-qc/1306.2082

  22. Momeni, D., Raza, M., Myrzakulov, R.: Eur. Phys. J. Plus 129, 30 (2014)

    Article  Google Scholar 

  23. Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)

    Article  MATH  ADS  Google Scholar 

  24. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 77, 026007 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  25. Faraoni, V.: Phys. Rev. D 74, 104017 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  26. Sawicki, I., Hu, W.: Phys. Rev. D 75, 127502 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  27. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  28. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 652, 343 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  29. Akbar, M., Cai, R.G.: Phys. Lett. B 635, 7 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  30. Akbar, M., Cai, R.G.: Phys. Lett. B 648, 243 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  31. Corda, C.: Astropart. Phys. 34, 587 (2011)

    Article  ADS  Google Scholar 

  32. Corda, C.: Gen. Relativ. Gravit. 40, 2201 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  33. Cognola, G. et al.: Phys. Rev. D 77, 046009 (2008)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  35. Hendi, S.H.: Phys. Lett. B 690, 220 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  36. De Felice, A., Tsujikawa, S.: Living Rev. Rel. 13, 3 (2010)

    Google Scholar 

  37. Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007)

    Article  ADS  Google Scholar 

  38. Starobinsky, A.A.: JETP Lett. 86, 157 (2007)

    Article  ADS  Google Scholar 

  39. Dev, A. et al.: Phys. Rev. D 083515, 78 (2008)

    Google Scholar 

  40. Appleby, S.A., Battye, R.A.: Phys. Lett. B 654, 7 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  41. Tsujikawa, S.: Phys. Rev. D 77, 023507 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  42. Hodgkinson, L., Louko, J.: Phys. Rev. D 86, 064031 (2012)

    Article  ADS  Google Scholar 

  43. Moon, T., Myung, Y.S.: Phys. Rev. D 86, 124042 (2012)

    Article  ADS  Google Scholar 

  44. Eune, M., Kim, W., Yi, S.H.: JHEP 03, 020 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  45. Hendi, S.H.: JHEP 03, 065 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  46. Frodden, E., Geiller, M., Noui, K., Perez, A.: JHEP 05, 139 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  47. Carlip, S.: Class. Quantum Gravit. 12, 2853 (1995)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  48. Ashtekar, A., Wisniewski, J., Dreyer, O.: Adv. Theor. Math. Phys. 6, 507 (2002)

    MathSciNet  MATH  Google Scholar 

  49. Sarkar, T., Sengupta, G., Tiwari, B.N.: JHEP 11, 015 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  50. Witten, E.: Adv. Theor. Math. Phys 2, 505 (1998)

    MathSciNet  MATH  Google Scholar 

  51. Carlip, S.: Class. Quantum Gravit. 22, R85 (2005)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  52. Banados, M., Teitelboim, C., Zanelli, J.: Phys. Rev. Lett. 69, 1849 (1992)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  53. Banados, M., Henneaux, M., Teitelboim, C., Zanelli, J.: Phys. Rev. D 48, 1506 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  54. Nojiri, S., Odintsov, S.D.: Mod. Phys. Lett. A 13, 2695 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  55. Emparan, R., Horowitz, G.T., Myers, R.C.: JHEP 01, 021 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  56. Hemming, S., Vakkuri, E.K., Kraus, P.: JHEP 10, 006 (2002)

    Article  ADS  Google Scholar 

  57. Setare, M.R.: Class. Quantum Gravit. 21, 1453 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  58. Sahoo, B., Sen, A.: JHEP 07, 008 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  59. Setare, M.R.: Eur. Phys. J.C 49, 865 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  60. Cadoni, M., Setare, M.R.: JHEP 07, 131 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  61. Park, M.I.: Phys. Rev. D 77, 026011 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  62. Park, M.I.: Phys. Rev. D 77, 126012 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  63. Parsons, J., Ross, S.F.: JHEP 04, 134 (2009)

    Article  ADS  Google Scholar 

  64. Setare, M.R., Jamil, M.: Phys. Lett. B 681, 469 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  65. Witten, E. arXiv:gr-qc/0706.3359

  66. Cadoni, M., Setare, M.R.: JHEP 07, 131 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  67. Claessens, L. arXiv:gr-qc/0912.2245

  68. de Boer, J., Sheikh-Jabbari, M.M., Simon, J.: Class. Quantum Gravit. 28, 175012 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  69. Hyun, S.: J. Korean Phys. Soc. 33, S532 (1998)

    ADS  Google Scholar 

  70. Canfora, F., Giacomini, A.: Phys. Rev. D 82, 024022 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  71. Hendi, S.H.: Eur. Phys. J. C 71, 1551 (2011)

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  73. Hendi, S.H.: Eur. Phys. J. C 69, 281 (2010)

    Article  ADS  Google Scholar 

  74. One may see the Wald entropy \(S=\frac {A}{4\pi }(1+f_{R})\) vanishes for this theory

  75. York, J.W.: Phys. Rev. D 28, 2929 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  76. Zurek, W.H., Thorne, K.S.: Phys. Rev. Lett. 54, 2171 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  77. Wheeler, J.A.: A Journey into Gravity and Spacetime Freeman (N.Y.) (1990)

  78. ’t Hooft, G.: Phys. Nucl. B 335, 138 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  79. Frolov, V., Novikov, I.: Phys. Rev. D 48, 4545 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  80. Carlip, S.: Phys. Rev. D 51, 632 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  81. Cvetic, M., Tseytlin, A.: Phys. Rev. D 53, 5619 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  82. Strominger, A.: JHEP 02, 009 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  83. Hendi, S.H., Momeni, D.: Eur. Phys. J. C 71, 1823 (2011)

    Article  ADS  Google Scholar 

  84. Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)

    Article  MATH  ADS  Google Scholar 

  85. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  86. Faraoni, V.: Phys. Rev. D 74, 104017 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  87. Faraoni, V.: Phys. Rev. D 76, 127501 (2007)

    Article  ADS  Google Scholar 

  88. Bertolami, O., Sequeira, M.C.: Phys. Rev. D 79, 104010 (2009)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

We are grateful to M. H. Vahidinia and H. Mohammadpour for reading the manuscript. We also wish to thank Shiraz University Research Council. This work has been supported financially by Research Institute for Astronomy & Astrophysics of Maragha (RIAAM), Iran.

Author information

Authors and Affiliations

  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran

    S. H. Hendi

  2. Research Institute for Astrophysics and Astronomy of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

    S. H. Hendi

Authors
  1. S. H. Hendi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. H. Hendi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hendi, S.H. (2 + 1)-Dimensional Solutions in F(R) Gravity. Int J Theor Phys 53, 4170–4181 (2014). https://doi.org/10.1007/s10773-014-2168-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2168-8

Keywords

Search

Navigation