Abstract
It has recently been demonstrated that the dynamics of black holes at large D can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape S D−p−2×R p,1. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as D is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory-Laflamme instability and its end point, exactly agree with the effective dynamical ‘black brane’ equations of Emparan Suzuki and Tanabe. Our results thus identify the ‘black brane’ equations as a special limit of the membrane equations and so unify these approaches to large D black hole dynamics.
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References
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, Holographic superconductivity in the large D expansion, JHEP 01 (2014) 145 [arXiv:1312.1108] [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].
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].
R. Emparan, R. Suzuki and K. Tanabe, Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion, JHEP 04 (2015) 085 [arXiv:1502.02820] [INSPIRE].
G. Giribet, Large D limit of dimensionally continued gravity, Phys. Rev. D 87 (2013) 107504 [arXiv:1303.1982] [INSPIRE].
P. Dominis Prester, Small black holes in the large D limit, JHEP 06 (2013) 070 [arXiv:1304.7288] [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].
Y. Dandekar, A. De, S. Mazumdar, S. Minwalla and A. Saha, The large D black hole Membrane Paradigm at first subleading order, 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].
K. Tanabe, Black rings at large D, JHEP 02 (2016) 151 [arXiv:1510.02200] [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].
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].
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].
K. Tanabe, Elastic instability of black rings at large D, arXiv:1605.08116 [INSPIRE].
K. Tanabe, Charged rotating black holes at large D, arXiv:1605.08854 [INSPIRE].
A. Sadhu and V. Suneeta, Nonspherically symmetric black string perturbations in the large dimension limit, Phys. Rev. D 93 (2016) 124002 [arXiv:1604.00595] [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 and A. Vincart-Emard, On Brane Instabilities in the Large D Limit, JHEP 08 (2016) 166 [arXiv:1607.01747] [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 and P.-C. Li, Instability of Charged Gauss-Bonnet Black Hole in de Sitter Spacetime at Large D, arXiv:1607.04713 [INSPIRE].
S. Bhattacharyya, S. Minwalla and S.R. Wadia, The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity, JHEP 08 (2009) 059 [arXiv:0810.1545] [INSPIRE].
J. Camps, R. Emparan and N. Haddad, Black Brane Viscosity and the Gregory-Laflamme Instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
M.M. Caldarelli, J. Camps, B. Goutéraux and K. Skenderis, AdS/Ricci-flat correspondence and the Gregory-Laflamme instability, Phys. Rev. D 87 (2013) 061502 [arXiv:1211.2815] [INSPIRE].
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ArXiv ePrint: 1609.02912
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Dandekar, Y., Mazumdar, S., Minwalla, S. et al. Unstable ‘black branes’ from scaled membranes at large D. J. High Energ. Phys. 2016, 140 (2016). https://doi.org/10.1007/JHEP12(2016)140
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DOI: https://doi.org/10.1007/JHEP12(2016)140