International Journal of Theoretical Physics

, Volume 55, Issue 2, pp 892–900 | Cite as

Effective Potential in Noncommutative BTZ Black Hole

  • Jafar Sadeghi
  • Vahid Reza Shajiee


In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.


BTZ black hole Noncommutative Geodesic Effective potential 


  1. 1.
    Doplicher, S., Fredenhagen, K., Roberts, J.E.: The quantum structure of spacetime at the planck scale and quantum fields. Commun. Math. Phys. 172.1, 187–220 (1995)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Rovelli, C, Smolin, L: Discreteness of area and volume in quantum gravity. Nucl. Phys. B 442.3, 593–619 (1995)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Hooft, G. T.: Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026 (1993)
  4. 4.
    Giudice, G.F., Rattazzi, R., Wells, J.D.: Quantum gravity and extra dimensions at high-energy colliders. Nucl. Phys. B 544.1, 3–38 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    Aschieri, P., et al.: A gravity theory on noncommutative spaces. Classical Quantum Grav. 22.17, 3511 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Nicolini, P: Noncommutative black holes, the final appeal to quantum gravity: A review. Int. J. Modern Phys. A 24.07, 1229–1308 (2009)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Rivelles, V.O.: Noncommutative field theories and gravity. Phys. Lett. B 558.3, 191–196 (2003)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Banados, M., Teitelboim, C., Zanelli, J.: Black hole in three-dimensional spacetime. Phys. Rev. Lett. 69.13, 1849 (1992)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Maldacena, J.: Eternal black holes in anti-de sitter. J. High Energy Phys. 2003.04, 021 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chang-Young, E., Lee, D., Lee, Y.: The noncommutative BTZ black hole in polar coordinates. Classical Quantum Grav. 26.18, 185001 (2009)CrossRefGoogle Scholar
  11. 11.
    Kim, H.-C., et al.: Smeared BTZ black hole from space noncommutativity. J. High Energy Phys. 2008.10, 060 (2008)CrossRefGoogle Scholar
  12. 12.
    Banados, M., et al.: Geometry of the 2+ 1 black hole. Phys. Rev. D 48.4, 1506 (1993)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Carlip, S., Teitelboim, C.: Aspects of black hole quantum mechanics and thermodynamics in 2+ 1 dimensions. Phys. Rev. D 51.2, 622 (1995)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Seiberg, N., Witten, E.: String theory and noncommutative geometry. J. High Energy Phys. 1999, 09, 32 (1999)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Jahangir, R., Saifullah, K.: Thermodynamics of noncommutative BTZ black hole, arXiv:1101.6073 (2011)
  16. 16.
    Anacleto, M.A., Brito, F.A., Passos, E.: Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole, arXiv:1408.4481 (2014)
  17. 17.
    Cruz, N., Martinez, C., Pena, L.: Geodesic structure of the (2+ 1)-dimensional BTZ black hole. Classical Quantum Grav. 11.11, 2731 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of MazandaranBabolsarIran

Personalised recommendations