Skip to main content
SpringerLink
Log in

Black-hole solutions in F(R) gravity with conformal anomaly

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

Abstract

In this paper, we consider F(R)=R+f(R) theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of F(R) models. Calculation of Kretschmann scalar shows that there is a singularity located at r=0. The geometry of uncharged (charged) solution corresponds to the Schwarzschild (Reissner–Nordström) singularity. Further, we discuss the viability of our models in detail. We show that these models can be stable, depending on their parameters and in different epochs of the universe.

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. H.A. Buchdahl, Mon. Not. R. Astron. Soc. 150, 1 (1970)

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. S. Capozziello, V.F. Cardone, A. Troisi, J. Cosmol. Astropart. Phys. 0608, 001 (2006)

    Article  ADS  Google Scholar 

  4. S. Capozziello, V.F. Cardone, A. Troisi, Mon. Not. R. Astron. Soc. 375, 1423 (2007)

    Article  ADS  Google Scholar 

  5. C. Frgerio Martins, P. Salucci, Mon. Not. R. Astron. Soc. 381, 1103 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. S. Nojiri, S.D. Odintsov, arXiv:1008.4275

  8. E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 83, 086006 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  10. S.H. Hendi, B. Eslam Panah, S.M. Mousavi, Gen. Rel. Grav. doi:10.1007/s10714-011-1307-2 [arXiv:1102.0089]

  11. S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  13. G. Cognola et al., Phys. Rev. D 73, 084007 (2006)

    Article  ADS  Google Scholar 

  14. M.C.B. Abdalla, S. Nojiri, S.D. Odintsov, Class. Quantum Gravity 22, L35 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. K. Bamba, S.D. Odintsov, J. Cosmol. Astropart. Phys. 0804, 024 (2008)

    Article  ADS  Google Scholar 

  18. C. Corda, Astropart. Phys. 30, 209 (2008)

    Article  ADS  Google Scholar 

  19. C. Corda, Int. J. Mod. Phys. D 18, 2275 (2009)

    Article  ADS  MATH  Google Scholar 

  20. C. Corda, Eur. Phys. J. C 65, 257 (2010)

    Article  ADS  Google Scholar 

  21. C. Corda, Astropart. Phys. 34, 412 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  24. D.M. Capper, M.J. Duff, Nuovo Cimento A 23, 173 (1974)

    Article  ADS  Google Scholar 

  25. M.J. Duff, Nucl. Phys. B 125, 334 (1977)

    Article  ADS  Google Scholar 

  26. M.J. Duff, Class. Quantum Gravity 11, 1387 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. A.M. Polyakov, Phys. Lett. B 103, 207 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  28. L. Parker, in Recent Developments in Gravitation, ed. by M. Levy, S. Deser (Plenum, New York, 1979)

    Google Scholar 

  29. S.M. Christensen, S.A. Fulling, Phys. Rev. D 15, 2088 (1977)

    Article  ADS  Google Scholar 

  30. S.P. Robinson, F. Wilczek, Phys. Rev. Lett. 95, 011303 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Iso, H. Umetsu, F. Wilczek, Phys. Rev. Lett. 96, 151302 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  32. S. Nojiri, S.D. Odintsov, S. Zerbini, Phys. Rev. D 62, 064006 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  33. S.W. Hawking, T. Hertog, H.S. Reall, Phys. Rev. D 63, 083504 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  34. S. Nojiri, S.D. Odintsov, Phys. Lett. B 484, 119 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. S. Nojiri, S.D. Odintsov, Int. J. Mod. Phys. A 16, 1015 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. I. Brevik, S.D. Odintsov, Phys. Lett. B 475, 247 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. S. Nojiri, O. Obregon, S.D. Odintsov, Mod. Phys. Lett. A 14, 1309 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Nojiri, S.D. Odintsov, Int. J. Mod. Phys. A 15, 989 (2000)

    MathSciNet  ADS  MATH  Google Scholar 

  39. S. Nojiri, S.D. Odintsov, Int. J. Mod. Phys. A 14, 1293 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. S. Nojiri, S.D. Odintsov, Phys. Rev. D 59, 044026 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  41. E. Elizalde, S. Nojiri, S.D. Odintsov, Phys. Rev. D 59, 061501 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  42. R.G. Cai, L.M. Cao, N. Ohta, J. High Energy Phys. 1004, 082 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  43. V.A. Miransky, V.P. Gusynin, Prog. Theor. Phys. 81, 426 (1989)

    Article  ADS  Google Scholar 

  44. C. Sasaki, H.K. Lee, W.G. Paeng, M. Rho, Phys. Rev. D 84, 034011 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  46. S. Capozziello, S. Nojiri, S.D. Odintsov, Phys. Lett. B 634, 93 (2006)

    Article  ADS  Google Scholar 

  47. T. Faulkner, M. Tegmark, E.F. Bunn, Y. Mao, Phys. Rev. D 76, 063505 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  48. V. Faraoni, Phys. Rev. D 75, 067302 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  49. Y. Bisabr, Phys. Scr. 80, 045902 (2009)

    Article  ADS  Google Scholar 

  50. M. Capone, M.L. Ruggiero, Class. Quantum Gravity 27, 125006 (2010)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  53. T.R.P. Carames, E.R. Bezerra de Mello, Eur. Phys. J. C 64, 113 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. L. Sebastiani, S. Zerbini, Eur. Phys. J. C 71, 1591 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  56. S.W. Hawking, D.N. Page, Commun. Math. Phys. 87, 577 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  57. T. Ortin, Gravity and Strings (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  58. L. Vanzo, Phys. Rev. D 56, 6475 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  59. D.R. Brill, J. Louko, P. Peldan, Phys. Rev. D 56, 3600 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  60. R.B. Mann, Class. Quantum Gravity 14, 2927 (1997)

    Article  ADS  MATH  Google Scholar 

  61. C. Cherubini, D. Bini, S. Capozziello, R. Ruffini, Int. J. Mod. Phys. D 11, 827 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  62. E. Elizaldea, S.D. Odintsov, L. Sebastianid, S. Zerbini, arXiv:1108.6184 [gr-qc]

  63. V. Faraoni, Ann. Phys. 317, 366 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. V. Faraoni, Phys. Rev. D 72, 061501 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  65. G. Cognola, S. Zerbini, J. Phys. A 39, 6245 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  66. S. Nojiri, S.D. Odintsov, Phys. Rev. D 74, 086006 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  67. S. Nojiri, S.D. Odintsov, J. Phys. Conf. Ser. 66, 012005 (2007)

    Article  ADS  Google Scholar 

  68. L. Amendola, R. Gannouji, D. Polarski, S. Tsujikawa, Phys. Rev. D 75, 083504 (2007)

    Article  ADS  Google Scholar 

  69. V. Faraoni, Phys. Rev. D 75, 067302 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  70. D. Bazeia, B. Carneiro da Cunha, R. Menezes, A. Yu, Phys. Lett. B 649, 445 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  71. T. Randor, Phys. Rev. D 75, 064033 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  72. T. Randor, Phys. Lett. B 652, 228 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  73. L.M. Sokolowski, Class. Quantum Gravity 24, 3391 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  74. G. Cognola, M. Gastaldi, S. Zerbini, Int. J. Theor. Phys. 47, 898 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  76. S. Capozziello, S. Nojiri, S.D. Odintsov, A. Troisi, Phys. Lett. B 639, 135 (2006)

    Article  ADS  Google Scholar 

  77. V. Faraoni, Phys. Rev. D 72, 061501 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  78. S. Nojiri, S.D. Odintsov, Gen. Relativ. Gravit. 36, 1765 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  79. X.H. Meng, P. Wang, Phys. Lett. B 584, 1 (2004)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  81. S. Capozziello, S. Tsujikawa, Phys. Rev. D 77, 107501 (2008)

    Article  ADS  Google Scholar 

  82. P. Brax, C. van de Bruck, A.C. Davis, D.J. Shaw, Phys. Rev. D 78, 104021 (2008)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  84. L. Pogosian, A. Silvestri, Phys. Rev. D 77, 023503 (2008)

    Article  ADS  Google Scholar 

  85. V. Faraoni, Phys. Rev. D 75, 067302 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  86. A. Nunez, S. Solganik, arXiv:hep-th/0403159

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

    Article  ADS  Google Scholar 

  88. E.C. Thomas, F.R. Urban, A.R. Zhitnitsky, J. High Energy Phys. 0908, 043 (2009)

    Article  ADS  Google Scholar 

  89. R. Schutzhold, Phys. Rev. Lett. 89, 081302 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, College of Sciences, Yasouj University, Yasouj, 75914, Iran

    S. H. Hendi

  2. Department of Physics, Faculty of Sciences, Tarbiat Moa’llem University, Tehran, Iran

    D. Momeni

Authors
  1. S. H. Hendi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Momeni
    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

Cite this article

Hendi, S.H., Momeni, D. Black-hole solutions in F(R) gravity with conformal anomaly. Eur. Phys. J. C 71, 1823 (2011). https://doi.org/10.1140/epjc/s10052-011-1823-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjc/s10052-011-1823-y

Keywords

Search

Navigation