Abstract
We present a class of 3D black holes based on flat connections which are poly-nomials in the BTZ hs(λ) × hs(λ)-valued connection. We solve analytically the fluctuation equations of matter in their background and find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary two-point functions. We also relate our results and those arising in other backgrounds discussed recently in the literature on the subject.
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References
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
V. Cardoso and J.P.S. Lemos, Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3 − D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
M. Gutperle and P. Kraus, Higher Spin Black Holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, P. Kraus and E. Perlmutter, Scalar fields and three-point functions in D =3 higher spin gravity, JHEP 07 (2012) 113 [arXiv:1111.3926] [INSPIRE].
P. Kraus and E. Perlmutter, Probing higher spin black holes, JHEP 02 (2013) 096 [arXiv:1209.4937] [INSPIRE].
M. Beccaria and G. Macorini, Resummation of scalar correlator in higher spin black hole background, JHEP 02 (2014) 071 [arXiv:1311.5450] [INSPIRE].
M. Bañados, R. Canto and S. Theisen, The Action for higher spin black holes in three dimensions, JHEP 07 (2012) 147 [arXiv:1204.5105] [INSPIRE].
J.R. David, M. Ferlaino and S.P. Kumar, Thermodynamics of higher spin black holes in 3D, JHEP 11 (2012) 135 [arXiv:1210.0284] [INSPIRE].
M. Ferlaino, T. Hollowood and S.P. Kumar, Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3, Phys. Rev. D 88 (2013) 066010 [arXiv:1305.2011] [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Brief review on higher spin black holes, arXiv:1402.1465 [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Higher spin gravity in 3D: Black holes, global charges and thermodynamics, Phys. Lett. B 726 (2013) 444 [arXiv:1207.2844] [INSPIRE].
G. Compère and W. Song, W symmetry and integrability of higher spin black holes, JHEP 09 (2013) 144 [arXiv:1306.0014] [INSPIRE].
M. Gutperle, E. Hijano and J. Samani, Lifshitz black holes in higher spin gravity, JHEP 04 (2014) 020 [arXiv:1310.0837] [INSPIRE].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS 3, JHEP 01 (2014) 023 [arXiv:1302.0816] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
C. Bunster, M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Generalized Black Holes in Three-dimensional Spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
J. de Boer and J.I. Jottar, Boundary Conditions and Partition Functions in Higher Spin AdS 3 /CFT 2, arXiv:1407.3844 [INSPIRE].
V.E. Didenko, A.S. Matveev and M.A. Vasiliev, BTZ Black Hole as Solution of 3 − D Higher Spin Gauge Theory, Theor. Math. Phys. 153 (2007) 1487 [hep-th/0612161] [INSPIRE].
S. Monnier, Finite higher spin transformations from exponentiation, arXiv:1402.4486 [INSPIRE].
M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Chemical potentials in three-dimensional higher spin anti-de Sitter gravity, JHEP 12 (2013) 048 [arXiv:1309.4362] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: A review, J. Phys. A 46 (2013) 214001 [arXiv:1208.5182] [INSPIRE].
M. Gary, D. Grumiller, S. Prohazka and S.-J. Rey, Lifshitz Holography with Isotropic Scale Invariance, JHEP 08 (2014) 001 [arXiv:1406.1468] [INSPIRE].
Y. Ilyashenko and S. Yakovenko, Lectures On Analytic Differential Equations, first edition, AMS, New York (2008).
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Dover, Rhode Island, ninth dover printing, tenth gpo printing ed., (1964).
M.R. Gaberdiel, K. Jin and E. Perlmutter, Probing higher spin black holes from CFT, JHEP 10 (2013) 045 [arXiv:1307.2221] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
C.N. Pope, L.J. Romans and X. Shen, A New Higher Spin Algebra and the Lone Star Product, Phys. Lett. B 242 (1990) 401 [INSPIRE].
C. Hoyos and P. Koroteev, On the Null Energy Condition and Causality in Lifshitz Holography, Phys. Rev. D 82 (2010) 084002 [Erratum ibid. D 82 (2010) 109905] [arXiv:1007.1428] [INSPIRE].
P. Koroteev and M. Libanov, Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance, Phys. Rev. D 79 (2009) 045023 [arXiv:0901.4347] [INSPIRE].
I. Amado, C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Hydrodynamics and beyond in the strongly coupled N =4 plasma, JHEP 07 (2008) 133 [arXiv:0805.2570] [INSPIRE].
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ArXiv ePrint: 1407.5203v2
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Cabo-Bizet, A., Gava, E., Giraldo-Rivera, V.I. et al. Black holes in the 3D higher spin theory and their quasi normal modes. J. High Energ. Phys. 2014, 13 (2014). https://doi.org/10.1007/JHEP11(2014)013
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DOI: https://doi.org/10.1007/JHEP11(2014)013