Abstract
We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k9 for the sound mode and to k8 for the shear mode.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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] [INSPIRE].
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].
R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP 07 (2014) 113 [arXiv:1406.1258] [INSPIRE].
V. Asnin, D. Gorbonos, S. Hadar, et al., High and Low Dimensions in The Black Hole Negative Mode, Class. Quant. Grav. 24 (2007) 5527 [arXiv:0706.1555] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, The large D limit of General Relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].
R. Emparan, D. Grumiller and K. Tanabe, Large-D gravity and low-D strings, Phys. Rev. Lett. 110 (2013) 251102 [arXiv:1303.1995] [INSPIRE].
R. Emparan and K. Tanabe, Universal quasinormal modes of large D black holes, Phys. Rev. D 89 (2014) 064028 [arXiv:1401.1957] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Instability of rotating black holes: large D analysis, JHEP 06 (2014) 106 [arXiv:1402.6215] [INSPIRE].
Ó.J.C. Dias, G.S. Hartnett and J.E. Santos, Quasinormal modes of asymptotically flat rotating black holes, Class. Quant. Grav. 31 (2014) 245011 [arXiv:1402.7047] [INSPIRE].
M.M. Caldarelli, J. Camps, B. Goutéraux, et al., AdS/Ricci-flat correspondence and the Gregory-Laflamme instability, Phys. Rev. D 87 (2013) 061502 [arXiv:1211.2815] [INSPIRE].
M.M. Caldarelli, J. Camps, B. Goutéraux and K. Skenderis, AdS/Ricci-flat correspondence, JHEP 04 (2014) 071 [arXiv:1312.7874] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
S. Bhattacharyya, R. Loganayagam, I. Mandal, S. Minwalla and A. Sharma, Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions, JHEP 12 (2008) 116 [arXiv:0809.4272] [INSPIRE].
H. Kodama and A. Ishibashi, A Master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions, Prog. Theor. Phys. 110 (2003) 701 [hep-th/0305147] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, Hydrodynamic Gradient Expansion in Gauge Theory Plasmas, Phys. Rev. Lett. 110 (2013) 211602 [arXiv:1302.0697] [INSPIRE].
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black Rings in (Anti)-deSitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [INSPIRE].
J. Armas and N.A. Obers, Blackfolds in (Anti)-de Sitter Backgrounds, Phys. Rev. D 83 (2011) 084039 [arXiv:1012.5081] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1502.02820
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Emparan, R., Suzuki, R. & Tanabe, K. Quasinormal modes of (anti-)de Sitter black holes in the 1/D expansion. J. High Energ. Phys. 2015, 85 (2015). https://doi.org/10.1007/JHEP04(2015)085
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)085