Abstract
In this note, we have extended the result of [1] to calculate the membrane stress tensor up to \( \mathcal{O}\left(\frac{1}{D}\right) \) localized on the co-dimension one membrane world volume propagating in asymptotically flat/AdS/dS spacetime. We have shown that the subleading order membrane equation follows from the conservation equation of this stress tensor.
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S. Bhattacharyya et al., Currents and Radiation from the large D Black Hole Membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [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, 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, 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].
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].
S. Bhattacharyya, P. Biswas and Y. Dandekar, Black holes in presence of cosmological constant: second order in\( \frac{1}{D} \), JHEP 10 (2018) 171 [arXiv:1805.00284] [INSPIRE].
P. Dominis Prester, Small black holes in the large D limit, JHEP 06 (2013) 070 [arXiv:1304.7288] [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, Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion, JHEP 04 (2015) 085 [arXiv:1502.02820] [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, S. Mazumdar, S. Minwalla and A. Saha, Unstable ‘black branes’ from scaled membranes at large D, JHEP 12 (2016) 140 [arXiv:1609.02912] [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, Black rings at large D, JHEP 02 (2016) 151 [arXiv:1510.02200] [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].
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].
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].
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].
K. Tanabe, Charged rotating black holes at large D, arXiv:1605.08854 [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 and P.-C. Li, Instability of Charged Gauss-Bonnet Black Hole in de Sitter Spacetime at Large D, arXiv:1607.04713 [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].
M. Rozali, E. Sabag and A. Yarom, Holographic Turbulence in a Large Number of Dimensions, JHEP 04 (2018) 065 [arXiv:1707.08973] [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].
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].
A. Kar, T. Mandal and A. Saha, The large D membrane paradigm for general four-derivative theory of gravity with a cosmological constant, JHEP 08 (2019) 078 [arXiv:1904.08273] [INSPIRE].
Y. Dandekar and A. Saha, Large D membrane for Higher Derivative Gravity and Black Hole Second Law, JHEP 02 (2020) 083 [arXiv:1910.10964] [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].
S. Bhattacharyya, P. Biswas and M. Patra, A leading-order comparison between fluid-gravity and membrane-gravity dualities, JHEP 05 (2019) 022 [arXiv:1807.05058] [INSPIRE].
S. Bhattacharyya, P. Biswas, A. Dinda and M. Patra, Fluid-gravity and membrane-gravity dualities — Comparison at subleading orders, JHEP 05 (2019) 054 [arXiv:1902.00854] [INSPIRE].
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Biswas, P. Stress tensor for large-D membrane at subleading orders. J. High Energ. Phys. 2020, 110 (2020). https://doi.org/10.1007/JHEP07(2020)110
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DOI: https://doi.org/10.1007/JHEP07(2020)110