Abstract
We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations for stationary black holes and the spectrum of linearised spectrum about black string configurations has been obtained using the membrane equation for EGB gravity. All our results are worked out to linear order in the Gauss-Bonnet parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP 04 (2016) 076 [arXiv:1504.06613] [INSPIRE].
S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, JHEP 04 (2016) 128 [arXiv:1511.03432] [INSPIRE].
S. Bhattacharyya, P. Biswas, B. Chakrabarty, Y. Dandekar and A. Dinda, The large D black hole dynamics in AdS/dS backgrounds, JHEP 10 (2018) 033 [arXiv:1704.06076] [INSPIRE].
S. Bhattacharyya, P. Biswas and Y. Dandekar, Black holes in presence of cosmological constant: second order in 1/D, JHEP 10 (2018) 171 [arXiv:1805.00284] [INSPIRE].
Y. Dandekar, A. De, S. Mazumdar, S. Minwalla and A. Saha, The large D black hole membrane paradigm at first subleading order, JHEP 12 (2016) 113 [arXiv:1607.06475] [INSPIRE].
R. Emparan, T. Shiromizu, R. Suzuki, K. Tanabe and T. Tanaka, Effective theory of black holes in the 1/D expansion, JHEP 06 (2015) 159 [arXiv:1504.06489] [INSPIRE].
R. Suzuki and K. Tanabe, Stationary black holes: large D analysis, JHEP 09 (2015) 193 [arXiv:1505.01282] [INSPIRE].
R. Suzuki and K. Tanabe, Non-uniform black strings and the critical dimension in the 1/D expansion, JHEP 10 (2015) 107 [arXiv:1506.01890] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Evolution and end point of the black string instability: large D solution, Phys. Rev. Lett. 115 (2015) 091102 [arXiv:1506.06772] [INSPIRE].
K. Tanabe, Instability of the de Sitter Reissner-Nordstrom black hole in the 1/D expansion, Class. Quant. Grav. 33 (2016) 125016 [arXiv:1511.06059] [INSPIRE].
Y. Dandekar, S. Mazumdar, S. Minwalla and A. Saha, Unstable ‘black branes’ from scaled membranes at large D, JHEP 12 (2016) 140 [arXiv:1609.02912] [INSPIRE].
Y. Dandekar, S. Kundu, S. Mazumdar, S. Minwalla, A. Mishra and A. Saha, An action for and hydrodynamics from the improved large D membrane, JHEP 09 (2018) 137 [arXiv:1712.09400] [INSPIRE].
R. Emparan, K. Izumi, R. Luna, R. Suzuki and K. Tanabe, Hydro-elastic complementarity in black branes at large D, JHEP 06 (2016) 117 [arXiv:1602.05752] [INSPIRE].
C.P. Herzog, M. Spillane and A. Yarom, The holographic dual of a Riemann problem in a large number of dimensions, JHEP 08 (2016) 120 [arXiv:1605.01404] [INSPIRE].
M. Rozali, E. Sabag and A. Yarom, Holographic turbulence in a large number of dimensions, JHEP 04 (2018) 065 [arXiv:1707.08973] [INSPIRE].
M. Rozali and A. Vincart-Emard, On brane instabilities in the large D limit, JHEP 08 (2016) 166 [arXiv:1607.01747] [INSPIRE].
C.P. Herzog and Y. Kim, The large dimension limit of a small black hole instability in anti-de Sitter space, JHEP 02 (2018) 167 [arXiv:1711.04865] [INSPIRE].
B. Chen, Z.-Y. Fan, P. Li and W. Ye, Quasinormal modes of Gauss-Bonnet black holes at large D, JHEP 01 (2016) 085 [arXiv:1511.08706] [INSPIRE].
B. Chen, P.-C. Li and Z.-Z. Wang, Charged black rings at large D, JHEP 04 (2017) 167 [arXiv:1702.00886] [INSPIRE].
B. Chen and P.-C. Li, Static Gauss-Bonnet black holes at large D, JHEP 05 (2017) 025 [arXiv:1703.06381] [INSPIRE].
B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet black strings at large D, JHEP 10 (2017) 123 [arXiv:1707.09766] [INSPIRE].
B. Chen, P.-C. Li, Y. Tian and C.-Y. Zhang, Holographic turbulence in Einstein-Gauss-Bonnet gravity at large D, arXiv:1804.05182 [INSPIRE].
M. Mandlik and S. Thakur, Stationary solutions from the large D membrane paradigm, JHEP 11 (2018) 026 [arXiv:1806.04637] [INSPIRE].
Y. Choquet-Bruhat, The Cauchy problem for stringy gravity, J. Math. Phys. 29 (1988) 1891 [INSPIRE].
S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [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: 1806.05201
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Saha, A. The large D membrane paradigm for Einstein-Gauss-Bonnet gravity. J. High Energ. Phys. 2019, 28 (2019). https://doi.org/10.1007/JHEP01(2019)028
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)028