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Generalized (2+1) dimensional black hole by Noether symmetry

  • F. DarabiEmail author
  • K. Atazadeh
  • A. Rezaei-Aghdam
Regular Article - Theoretical Physics

Abstract

We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D 1 R(n/n+1)(R/K)1/n +D 2 R+D 3, where the constant term D 3 plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D 1=0,D 2=1, namely f(R)=R+D 3, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D 3 and represents symmetry of the action under the transformation RR′=R+D 3 along the killing vector R . The ordinary BTZ black hole is obtained as the special case where D 3 is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy–Verlinde formula.

Keywords

Black Hole Black Hole Solution Killing Vector Ricci Scalar Conformal Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgement

This work has been supported financially by Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM) under research project NO.1/2782-76.

References

  1. 1.
    E.J. Martinec, Phys. Rev. D 30, 1198 (1984) ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Achúcarro, P.K. Townsend, Phys. Lett. B 180, 89 (1986) ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    E. Witten, Nucl. Phys. B 311, 46 (1988) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    E. Witten, Commun. Math. Phys. 121, 351 (1989) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    D. Ida, Phys. Rev. Lett. 85, 3758 (2000) ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Bañados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    M. Bañados, M. Henneaux, C. Teitelboim, J. Zanelli, Phys. Rev. D48, 1506 (1993) ADSGoogle Scholar
  8. 8.
    J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) ADSzbMATHMathSciNetGoogle Scholar
  9. 9.
    L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    H. Saida, J. Soda, Phys. Lett. B 471, 358 (2000) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    H. Saida, J. Soda, arXiv:gr-qc/0011095
  13. 13.
    S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011) ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    S. Tsujikawa, Lectures on cosmology: accelerated expansion of the universe, in Lectures Notes in Physics, vol. 800 (Springer, New York, 2010), pp. 99–145 Google Scholar
  18. 18.
    S. Capozziello, M. De Laurentis, Phys. Rep. 509, 167–321 (2011) ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    M. Demianski, R. de Ritis, C. Rubano, P. Scudellaro, Phys. Rev. D 46, 1391 (1992) ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    S. Capozziello, A. De Felice, J. Cosmol. Astropart. Phys. 0808, 016 (2008) ADSCrossRefGoogle Scholar
  21. 21.
    B. Vakili, Phys. Lett. B 669, 206 (2008) ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    H. Wei, X.-J. Guo, L.-F. Wang, Phys. Lett. B 707, 298 (2012) ADSCrossRefGoogle Scholar
  23. 23.
    K. Atazadeh, F. Darabi, Eur. Phys. J. C 72, 2016 (2012) ADSCrossRefGoogle Scholar
  24. 24.
    S. Capozziello, N. Frusciante, D. Vernieri, New spherically symmetric solutions in f(R)-gravity by Noether symmetries. arXiv:1204.4650
  25. 25.
    E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998) zbMATHMathSciNetGoogle Scholar
  26. 26.
    J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973) ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    J.D. Bekenstein, Phys. Rev. D 9, 3292 (1974) ADSCrossRefGoogle Scholar
  28. 28.
    S.W. Hawking, Phys. Rev. D 13, 191 (1976) ADSCrossRefMathSciNetGoogle Scholar
  29. 29.
    E. Verlinde, On the holographic principle in a radiation dominated universe. hep-th/0008140
  30. 30.
    J.L. Cardy, Nucl. Phys. B 270, 186 (1986) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    D. Klemm, A.C. Petkou, G. Siopsis, Nucl. Phys. B 601, 380 (2001) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  32. 32.
    R.-G. Cai, Phys. Rev. D 63, 124018 (2001) ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM)MaraghaIran
  2. 2.Department of PhysicsAzarbaijan Shahid Madani UniversityTabrizIran

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