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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [SPIRES].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Ann. Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [SPIRES].
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].
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].
E. Witten, Three-Dimensional Gravity Revisited, arXiv:0706.3359 [SPIRES].
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].
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].
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].
W. Li, W. Song and A. Strominger, Chiral Gravity in Three Dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [SPIRES].
D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [SPIRES].
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].
M.-i. Park, Constraint Dynamics and Gravitons in Three Dimensions, JHEP 09 (2008) 084 [arXiv:0805.4328] [SPIRES].
D. Grumiller, R. Jackiw and N. Johansson, Canonical analysis of cosmological topologically massive gravity at the chiral point, arXiv:0806.4185 [SPIRES].
S. Carlip, S. Deser, A. Waldron and D.K. Wise, Topologically Massive AdS Gravity, Phys. Lett. B 666 (2008) 272 [arXiv:0807.0486] [SPIRES].
S. Carlip, The Constraint Algebra of Topologically Massive AdS Gravity, JHEP 10 (2008) 078 [arXiv:0807.4152] [SPIRES].
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].
M. Blagojevic and B. Cvetkovic, Canonical structure of topologically massive gravity with a cosmological constant, JHEP 05 (2009) 073 [arXiv:0812.4742] [SPIRES].
W. Li, W. Song and A. Strominger, Comment on ’Cosmological Topological Massive Gravitons and Photons’, arXiv:0805.3101 [SPIRES].
A. Maloney, W. Song and A. Strominger, Chiral Gravity, Log Gravity and Extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [SPIRES].
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].
E. Ayon-Beato and M. Hassaine, pp waves of conformal gravity with self-interacting source, Ann. Phys. 317 (2005) 175 [hep-th/0409150] [SPIRES].
E. Ayon-Beato and M. Hassaine, Exploring AdS waves via nonminimal coupling, Phys. Rev. D 73 (2006) 104001 [hep-th/0512074] [SPIRES].
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].
D. Grumiller and I. Sachs, AdS 3 /LCFT 2 — Correlators in Cosmological Topologically Massive Gravity, JHEP 03 (2010) 012 [arXiv:0910.5241] [SPIRES].
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].
V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B 410 (1993) 535 [hep-th/9303160] [SPIRES].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [SPIRES].
E. Ayon-Beato, G. Giribet and M. Hassaine, Bending AdS Waves with New Massive Gravity, JHEP 05 (2009) 029 [arXiv:0904.0668] [SPIRES].
D. Grumiller and O. Hohm, AdS 3 /LCFT 2 -Correlators in New Massive Gravity, Phys. Lett. B 686 (2010) 264 [arXiv:0911.4274] [SPIRES].
M. Alishahiha and A. Naseh, Holographic Renormalization of New Massive Gravity, arXiv:1005.1544 [SPIRES].
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].
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].
M. Alishahiha, A. Naseh and H. Soltanpanahi, On Born-Infeld Gravity in Three Dimensions, Phys. Rev. D 82 (2010) 024042 [arXiv:1006.1757] [SPIRES].
H.R. Afshar, M. Alishahiha and A. Naseh, On three dimensional bigravity, Phys. Rev. D 81 (2010) 044029 [arXiv:0910.4350] [SPIRES].
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].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].
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].
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].
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].
I. Sachs and S.N. Solodukhin, Quasi-Normal Modes in Topologically Massive Gravity, JHEP 08 (2008) 003 [arXiv:0806.1788] [SPIRES].
I. Sachs, Quasi-Normal Modes for Logarithmic Conformal Field Theory, JHEP 09 (2008) 073 [arXiv:0807.1844] [SPIRES].
H.W. Lee, Y.-W. Kim and Y.S. Myung, Quasinormal modes for topologically massive black hole, arXiv:0807.1371 [SPIRES].
J. Crisostomo, S. Lepe and J. Saavedra, Quasinormal modes of extremal BTZ black hole, Class. Quant. Grav. 21 (2004) 2801 [hep-th/0402048] [SPIRES].
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].
G. Compere, S. de Buyl and S. Detournay, Non-Einstein geometries in Chiral Gravity, arXiv:1006.3099 [SPIRES].
I.D. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press Inc, U.S.A. (1965).
M. Bañados, Three-dimensional quantum geometry and black holes, hep-th/9901148 [SPIRES].
S. Carlip, Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1006.4468
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2010)081