Abstract
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.
Similar content being viewed by others
References
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)
Rovelli, C, Smolin, L: Discreteness of area and volume in quantum gravity. Nucl. Phys. B 442.3, 593–619 (1995)
Hooft, G. T.: Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026 (1993)
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)
Aschieri, P., et al.: A gravity theory on noncommutative spaces. Classical Quantum Grav. 22.17, 3511 (2005)
Nicolini, P: Noncommutative black holes, the final appeal to quantum gravity: A review. Int. J. Modern Phys. A 24.07, 1229–1308 (2009)
Rivelles, V.O.: Noncommutative field theories and gravity. Phys. Lett. B 558.3, 191–196 (2003)
Banados, M., Teitelboim, C., Zanelli, J.: Black hole in three-dimensional spacetime. Phys. Rev. Lett. 69.13, 1849 (1992)
Maldacena, J.: Eternal black holes in anti-de sitter. J. High Energy Phys. 2003.04, 021 (2003)
Chang-Young, E., Lee, D., Lee, Y.: The noncommutative BTZ black hole in polar coordinates. Classical Quantum Grav. 26.18, 185001 (2009)
Kim, H.-C., et al.: Smeared BTZ black hole from space noncommutativity. J. High Energy Phys. 2008.10, 060 (2008)
Banados, M., et al.: Geometry of the 2+ 1 black hole. Phys. Rev. D 48.4, 1506 (1993)
Carlip, S., Teitelboim, C.: Aspects of black hole quantum mechanics and thermodynamics in 2+ 1 dimensions. Phys. Rev. D 51.2, 622 (1995)
Seiberg, N., Witten, E.: String theory and noncommutative geometry. J. High Energy Phys. 1999, 09, 32 (1999)
Jahangir, R., Saifullah, K.: Thermodynamics of noncommutative BTZ black hole, arXiv:1101.6073 (2011)
Anacleto, M.A., Brito, F.A., Passos, E.: Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole, arXiv:1408.4481 (2014)
Cruz, N., Martinez, C., Pena, L.: Geodesic structure of the (2+ 1)-dimensional BTZ black hole. Classical Quantum Grav. 11.11, 2731 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sadeghi, J., Shajiee, V.R. Effective Potential in Noncommutative BTZ Black Hole. Int J Theor Phys 55, 892–900 (2016). https://doi.org/10.1007/s10773-015-2732-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-015-2732-x