Abstract
It has recently been shown that the dynamics of black holes in large number of dimensions D can be recast as the dynamics of a probe membrane propagating in the background spacetime which solves Einstein equations without matter. The equations of motion of this membrane are simply the statement of conservation of the stress tensor and charge current defined on this membrane. In this paper we obtain the effective equations of motion for stationary membranes in any empty background both in presence and absence of charge. It turns out that the thermodynamic quantities associated with the stationary membranes that satisfy these effective equations also satisfy the first law of black hole thermodynamics. These stationary membrane equations have some interesting solutions such as charged rotating black holes in flat and AdS backgrounds as well as black ring solutions in large D.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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, 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 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, Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion, JHEP 04 (2015) 085 [arXiv:1502.02820] [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, 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. 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].
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].
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].
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, 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, arXiv:1805.00284 [INSPIRE].
S. Kundu and P. Nandi, Large D gravity and charged membrane dynamics with nonzero cosmological constant, arXiv:1806.08515 [INSPIRE].
S. Bhattacharyya et al., Currents and Radiation from the large D Black Hole Membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [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].
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].
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 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].
M. Raman, Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes, JHEP 12 (2017) 144 [arXiv:1711.00287] [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].
R. Emparan, R. Luna, M. Martínez, R. Suzuki and K. Tanabe, Phases and Stability of Non-Uniform Black Strings, JHEP 05 (2018) 104 [arXiv:1802.08191] [INSPIRE].
B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet Black Rings at Large D, JHEP 07 (2018) 067 [arXiv:1805.03345] [INSPIRE].
T. Andrade, C. Pantelidou and B. Withers, Large D holography with metric deformations, JHEP 09 (2018) 138 [arXiv:1806.00306] [INSPIRE].
R. Suzuki and K. Tanabe, Stationary black holes: Large D analysis, JHEP 09 (2015) 193 [arXiv:1505.01282] [INSPIRE].
M.M. Caldarelli, O.J.C. Dias, R. Emparan and D. Klemm, Black Holes as Lumps of Fluid, JHEP 04 (2009) 024 [arXiv:0811.2381] [INSPIRE].
J. Armas and T. Harmark, Black Holes and Biophysical (Mem)-branes, Phys. Rev. D 90 (2014) 124022 [arXiv:1402.6330] [INSPIRE].
J. Armas and T. Harmark, Constraints on the effective fluid theory of stationary branes, JHEP 10 (2014) 063 [arXiv:1406.7813] [INSPIRE].
J. Armas, N.A. Obers and M. Sanchioni, Gravitational Tension, Spacetime Pressure and Black Hole Volume, JHEP 09 (2016) 124 [arXiv:1512.09106] [INSPIRE].
O.J.C. Dias, P. Figueras, R. Monteiro, H.S. Reall and J.E. Santos, An instability of higher-dimensional rotating black holes, JHEP 05 (2010) 076 [arXiv:1001.4527] [INSPIRE].
R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [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: 1806.04637
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
Mandlik, M., Thakur, S. Stationary solutions from the large D membrane paradigm. J. High Energ. Phys. 2018, 26 (2018). https://doi.org/10.1007/JHEP11(2018)026
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)026