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Quasi-normal modes of extremal BTZ black holes in TMG

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Abstract

We study the spectrum of tensor perturbations on extremal BTZ black holes in topologically massive gravity for arbitrary values of the coefficient of the Chern-Simons term, μ. Imposing proper boundary conditions at the boundary of the space and at the horizon, we find that the spectrum contains quasi-normal modes.

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References

  1. S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].

    Article  ADS  Google Scholar 

  2. S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [SPIRES].

  6. D. Orlando and L.I. Uruchurtu, Warped anti-de Sitter spaces from brane intersections in type-II string theory, JHEP 06 (2010) 049 [arXiv:1003.0712] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. D. Israel, C. Kounnas, D. Orlando and P.M. Petropoulos, Electric/magnetic deformations of S 3 and AdS 3 and geometric cosets, Fortsch. Phys. 53 (2005) 73 [hep-th/0405213] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. S. Detournay, D. Orlando, P.M. Petropoulos and P. Spindel, Three-dimensional black holes from deformed anti de Sitter, JHEP 07 (2005) 072 [hep-th/0504231] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. W. Li, W. Song and A. Strominger, Chiral Gravity in Three Dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [SPIRES].

    Article  ADS  Google Scholar 

  11. S. Carlip, S. Deser, A. Waldron and D.K. Wise, Cosmological Topologically Massive Gravitons and Photons, Class. Quant. Grav. 26 (2009) 075008 [arXiv:0803.3998] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. M.-i. Park, Constraint Dynamics and Gravitons in Three Dimensions, JHEP 09 (2008) 084 [arXiv:0805.4328] [SPIRES].

    Article  ADS  Google Scholar 

  13. D. Grumiller, R. Jackiw and N. Johansson, Canonical analysis of cosmological topologically massive gravity at the chiral point, arXiv:0806.4185 [SPIRES].

  14. S. Carlip, S. Deser, A. Waldron and D.K. Wise, Topologically Massive AdS Gravity, Phys. Lett. B 666 (2008) 272 [arXiv:0807.0486] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. S. Carlip, The Constraint Algebra of Topologically Massive AdS Gravity, JHEP 10 (2008) 078 [arXiv:0807.4152] [SPIRES].

    Article  ADS  Google Scholar 

  16. G. Giribet, M. Kleban and M. Porrati, Topologically Massive Gravity at the Chiral Point is Not Chiral, JHEP 10 (2008) 045 [arXiv:0807.4703] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Blagojevic and B. Cvetkovic, Canonical structure of topologically massive gravity with a cosmological constant, JHEP 05 (2009) 073 [arXiv:0812.4742] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. W. Li, W. Song and A. Strominger, Comment on ’Cosmological Topological Massive Gravitons and Photons’, arXiv:0805.3101 [SPIRES].

  19. A. Maloney, W. Song and A. Strominger, Chiral Gravity, Log Gravity and Extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, W hat is a chiral 2D CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [SPIRES].

    Article  ADS  Google Scholar 

  21. E. Ayon-Beato and M. Hassaine, pp waves of conformal gravity with self-interacting source, Ann. Phys. 317 (2005) 175 [hep-th/0409150] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. E. Ayon-Beato and M. Hassaine, Exploring AdS waves via nonminimal coupling, Phys. Rev. D 73 (2006) 104001 [hep-th/0512074] [SPIRES].

    ADS  Google Scholar 

  23. K. Skenderis, M. Taylor and B.C. van Rees, Topologically Massive Gravity and the AdS/CFT Correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [SPIRES].

    Article  ADS  Google Scholar 

  24. D. Grumiller and I. Sachs, AdS 3 /LCFT 2 — Correlators in Cosmological Topologically Massive Gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].

    MATH  MathSciNet  ADS  Google Scholar 

  26. V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. E. Ayon-Beato, G. Giribet and M. Hassaine, Bending AdS Waves with New Massive Gravity, JHEP 05 (2009) 029 [arXiv:0904.0668] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. D. Grumiller and O. Hohm, AdS 3 /LCFT 2 -Correlators in New Massive Gravity, Phys. Lett. B 686 (2010) 264 [arXiv:0911.4274] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. M. Alishahiha and A. Naseh, Holographic Renormalization of New Massive Gravity, arXiv:1005.1544 [SPIRES].

  31. S. Nam, J.-D. Park and S.-H. Yi, AdS Black Hole Solutions in the Extended New Massive Gravity, JHEP 07 (2010) 058 [arXiv:1005.1619] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. I. Gullu, T.C. Sisman and B. Tekin, Born-Infeld extension of new massive gravity, Class. Quant. Grav. 27 (2010) 162001 [arXiv:1003.3935] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. M. Alishahiha, A. Naseh and H. Soltanpanahi, On Born-Infeld Gravity in Three Dimensions, Phys. Rev. D 82 (2010) 024042 [arXiv:1006.1757] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  34. H.R. Afshar, M. Alishahiha and A. Naseh, On three dimensional bigravity, Phys. Rev. D 81 (2010) 044029 [arXiv:0910.4350] [SPIRES].

    ADS  Google Scholar 

  35. P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [SPIRES].

    Article  ADS  Google Scholar 

  36. P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].

    ADS  Google Scholar 

  37. D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasi-normal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. R.A. Konoplya, Influence of the back reaction of the Hawking radiation upon black hole quasinormal modes, Phys. Rev. D 70 (2004) 047503 [hep-th/0406100] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  39. V. Cardoso and J.P.S. Lemos, Scalar, electromagnetic and Weyl perturbations of BTZ black holes: Quasi normal modes, Phys. Rev. D 63 (2001) 124015 [gr-qc/0101052] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  40. I. Sachs and S.N. Solodukhin, Quasi-Normal Modes in Topologically Massive Gravity, JHEP 08 (2008) 003 [arXiv:0806.1788] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. I. Sachs, Quasi-Normal Modes for Logarithmic Conformal Field Theory, JHEP 09 (2008) 073 [arXiv:0807.1844] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. H.W. Lee, Y.-W. Kim and Y.S. Myung, Quasinormal modes for topologically massive black hole, arXiv:0807.1371 [SPIRES].

  43. J. Crisostomo, S. Lepe and J. Saavedra, Quasinormal modes of extremal BTZ black hole, Class. Quant. Grav. 21 (2004) 2801 [hep-th/0402048] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  44. E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. G. Compere, S. de Buyl and S. Detournay, Non-Einstein geometries in Chiral Gravity, arXiv:1006.3099 [SPIRES].

  46. I.D. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press Inc, U.S.A. (1965).

    Google Scholar 

  47. M. Bañados, Three-dimensional quantum geometry and black holes, hep-th/9901148 [SPIRES].

  48. S. Carlip, Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. School of physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

    Hamid R. Afshar & Mohsen Alishahiha

  2. Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran

    Hamid R. Afshar & Amir E. Mosaffa

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  1. Hamid R. Afshar
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  2. Mohsen Alishahiha
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  3. Amir E. Mosaffa
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Correspondence to Hamid R. Afshar.

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ArXiv ePrint: 1006.4468

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Afshar, H.R., Alishahiha, M. & Mosaffa, A.E. Quasi-normal modes of extremal BTZ black holes in TMG. J. High Energ. Phys. 2010, 81 (2010). https://doi.org/10.1007/JHEP08(2010)081

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