Skip to main content
Log in

A noncommutative model of BTZ spacetime

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

Abstract

We analyze a noncommutative model of BTZ spacetime based on deformation of the standard symplectic structure of phase space, i.e., a modification of the standard commutation relations among coordinates and momenta in phase space. We find a BTZ-like solution that is nonperturbative in the non-trivial noncommutative structure. It is shown that the use of deformed commutation relations in the modified non-canonical phase space eliminates the horizons of the standard metric.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. J.D. Barrow, A.B. Burd, D. Lancaster, Class. Quantum Gravity 3(4), 551 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  2. S. Deser, R. Jackiw, Ann. Phys. 153, 405 (1984). doi:10.1016/0003-4916(84)90025-3

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Deser, R. Jackiw, G. ’t Hooft, Ann. Phys. 152, 220 (1984). doi:10.1016/0003-4916(84)90085-X

    Article  ADS  Google Scholar 

  4. G. ’t Hooft, Commun. Math. Phys. 117, 685 (1988). doi:10.1007/BF01218392

    Article  ADS  MATH  Google Scholar 

  5. M. Bañados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992). doi:10.1103/PhysRevLett.69.1849

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Bañados, M. Henneaux, C. Teitelboim, J. Zanelli, Phys. Rev. D 48, 1506 (1993). doi:10.1103/PhysRevD.48.1506

    Article  MathSciNet  ADS  Google Scholar 

  7. S. Carlip, Class. Quantum Gravity 12, 2853 (1995). doi:10.1088/0264-9381/12/12/005

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. S. Carlip, Class. Quantum Gravity 22, R85 (2005). doi:10.1088/0264-9381/22/12/R01

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. P. Bieliavsky, S. Detournay, M. Rooman, P. Spindel, in 8èmes Rencontres Mathématiques de Glanon (2005). arXiv:hep-th/0511080

  10. A.A. Garcia, F.W. Hehl, C. Heinicke, A. Macias, Phys. Rev. D 67, 124016 (2003). doi:10.1103/PhysRevD.67.124016

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Cadoni, M.R. Setare, J. High Energy Phys. 0807, 131 (2008). doi:10.1088/1126-6708/2008/07/131

    Article  MathSciNet  ADS  Google Scholar 

  12. J.P.M. Pitelli, P.S. Letelier, Phys. Rev. D 77, 124030 (2008). doi:10.1103/PhysRevD.77.124030

    Article  MathSciNet  ADS  Google Scholar 

  13. J.M. Garcia-Islas, Class. Quantum Gravity 25, 245001 (2008). doi:10.1088/0264-9381/25/24/245001

    Article  MathSciNet  ADS  Google Scholar 

  14. E. Greenwood, E. Halstead, P. Hao, J. High Energy Phys. 1002, 044 (2010). doi:10.1007/JHEP02(2010)044

    Article  MathSciNet  ADS  Google Scholar 

  15. S. Carlip, Rep. Prog. Phys. 64, 885 (2001). doi:10.1088/0034-4885/64/8/301

    Article  MathSciNet  ADS  Google Scholar 

  16. J.W. Moffat, Phys. Lett. B 491, 345 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. P. Aschieri, C. Blohmann, M. Dimitrijević, F. Meyer, P. Schupp, J. Wess, Class. Quantum Gravity 22, 3511 (2005). doi:10.1088/0264-9381/22/17/011

    Article  ADS  MATH  Google Scholar 

  18. X. Calmet, A. Kobakhidze, Phys. Rev. D 72, 045010 (2005). doi:10.1103/PhysRevD.72.045010

    Article  MathSciNet  ADS  Google Scholar 

  19. M. Dobrski, Phys. Rev. D 84, 065005 (2011). doi:10.1103/PhysRevD.84.065005

    Article  ADS  Google Scholar 

  20. M. Chaichian, A. Tureanu, G. Zet, Phys. Lett. B 660, 573 (2008). doi:10.1016/j.physletb.2008.01.029

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. P. Nicolini, Int. J. Mod. Phys. A 24, 1229 (2009). doi:10.1142/S0217751X09043353

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. P. Schupp, S. Solodukhin, Exact black hole solutions in noncommutative gravity (2009). arXiv:0906.2724 [hep-th]

  23. D. Wang, R.B. Zhang, X. Zhang, Class. Quantum Gravity 26, 085014 (2009). doi:10.1088/0264-9381/26/8/085014

    Article  ADS  Google Scholar 

  24. M. Maceda, A. Macias, Phys. Rev. D 84, 064002 (2011). doi:10.1103/PhysRevD.84.064002

    Article  ADS  Google Scholar 

  25. M. Maceda, A. Macias, Phys. Lett. B 705, 157 (2011). doi:10.1016/j.physletb.2011.09.115

    Article  ADS  Google Scholar 

  26. N. Mebarki, F. Khelili, H. Bouhalouf, O. Mebarki, Electron. J. Theor. Phys. 6, 193 (2009)

    Google Scholar 

  27. A. Djemai, H. Smail, Commun. Theor. Phys. 41, 837 (2004)

    MathSciNet  MATH  Google Scholar 

  28. E.M. Abreu, C. Neves, W. Oliveira, Int. J. Mod. Phys. A 21, 5359 (2006). doi:10.1142/S0217751X06034094

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. A. Pachol, κ-Minkowski spacetime: mathematical formalism and applications in Planck scale physics. Ph.D. thesis, University of Wroclaw (2011)

  30. D. Kovacevic, S. Meljanac, A. Pachol, R. Strajn, Phys. Lett. B 711, 122 (2012). doi:10.1016/j.physletb.2012.03.062

    Article  MathSciNet  ADS  Google Scholar 

  31. B. Dolan, K.S. Gupta, A. Stern, Class. Quantum Gravity 24, 1647 (2007). doi:10.1088/0264-9381/24/6/017

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. M. Demetrian, P. Presnajder, A toy model for black hole in noncommutative spaces (2006). arXiv:gr-qc/0604113

  33. T.R. Govindarajan, S. Digal, K. Gupta, X. Martin, Phase structures in fuzzy geometries (2012). arXiv:1204.6165 [hep-th]

  34. A.H. Chamseddine, Int. J. Mod. Phys. A 16, 759 (2001). doi:10.1142/S0217751X01003883

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. C.L. Mantz, Holomorphic gravity: on the reciprocity of momentum and space. Master’s thesis, Spinoza Institute, Institute for Theoretical Physics, Utrecht University (2007)

  36. C.L. Mantz, T. Prokopec, Found. Phys. 41, 1597 (2011). doi:10.1007/s10701-011-9570-3

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Acknowledgements

We would like to thank the referee for her/his valuable comments on this work. We would also like to thank Alberto García for useful discussions and literature hints. This research was supported by CONACyT Grant No. 166041F3.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Maceda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maceda, M., Macías, A. A noncommutative model of BTZ spacetime. Eur. Phys. J. C 73, 2383 (2013). https://doi.org/10.1140/epjc/s10052-013-2383-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjc/s10052-013-2383-0

Keywords

Navigation