Abstract
Black rings are the black objects found in D spacetime dimensional gravity when D ≥ 5. These have event horizon topology SD−3 × S1. In this work the solutions of the large D membrane paradigm dual to stationary black rings in Einstein-Maxwell theory with or without cosmological constant are studied. It is shown that the first order membrane equations can only admit static asymptotically flat black rings, and the equilibrium angular velocity for the asymptotically AdS black rings at large D was obtained. The thermodynamic and dynamic stability of the asymptotically flat black ring solutions is studied. The apparent shortcomings of some of these results are argued to be curable within the large D membrane paradigm framework.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2011) [INSPIRE].
M.-l. Cai and G.J. Galloway, On the topology and area of higher dimensional black holes, Class. Quant. Grav. 18 (2001) 2707 [hep-th/0102149] [INSPIRE].
R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].
R.C. Myers, Myers-Perry black holes, arXiv:1111.1903 [INSPIRE].
R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].
R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
R. Emparan and H.S. Reall, Black rings, Class. Quant. Grav. 23 (2006) R169 [hep-th/0608012] [INSPIRE].
Y. Chervonyi, Towards higher dimensional black rings, Phys. Rev. D 92 (2015) 124037 [arXiv:1510.06041] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black rings in (Anti)-de Sitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [INSPIRE].
B. Kleihaus, J. Kunz and E. Radu, Black rings in six dimensions, Phys. Lett. B 718 (2013) 1073 [arXiv:1205.5437] [INSPIRE].
R. Emparan and C.P. Herzog, Large D limit of Einstein’s equations, Rev. Mod. Phys. 92 (2020) 045005 [arXiv:2003.11394] [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, 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].
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, 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].
T. Andrade, S.A. Gentle and B. Withers, Drude in D major, JHEP 06 (2016) 134 [arXiv:1512.06263] [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].
T. Andrade, C. Pantelidou and B. Withers, Large D holography with metric deformations, JHEP 09 (2018) 138 [arXiv:1806.00306] [INSPIRE].
T. Andrade, R. Emparan and D. Licht, Rotating black holes and black bars at large D, JHEP 09 (2018) 107 [arXiv:1807.01131] [INSPIRE].
R. Emparan and R. Suzuki, Topology-changing horizons at large D as Ricci flows, JHEP 07 (2019) 094 [arXiv:1905.01062] [INSPIRE].
T. Andrade, R. Emparan, D. Licht and R. Luna, Black hole collisions, instabilities, and cosmic censorship violation at large D, JHEP 09 (2019) 099 [arXiv:1908.03424] [INSPIRE].
D. Licht, R. Luna and R. Suzuki, Black ripples, flowers and dumbbells at large D, JHEP 04 (2020) 108 [arXiv:2002.07813] [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].
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, JHEP 01 (2019) 156 [arXiv:1804.05182] [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].
P.-C. Li, C.-Y. Zhang and B. Chen, The fate of instability of de Sitter black holes at large D, JHEP 11 (2019) 042 [arXiv:1909.02685] [INSPIRE].
M. Guo, P.-C. Li and B. Chen, Photon emission near Myers-Perry black holes in the large dimension limit, Phys. Rev. D 101 (2020) 024054 [arXiv:1911.08814] [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].
M. Rozali, E. Sabag and A. Yarom, Holographic turbulence in a large number of dimensions, JHEP 04 (2018) 065 [arXiv:1707.08973] [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].
M. Rozali and B. Way, Gravitating scalar stars in the large D limit, JHEP 11 (2018) 106 [arXiv:1807.10283] [INSPIRE].
J. Casalderrey-Solana, C.P. Herzog and B. Meiring, Holographic Bjorken flow at large-D, JHEP 01 (2019) 181 [arXiv:1810.02314] [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].
A. Sadhu and V. Suneeta, Schwarzschild-Tangherlini quasinormal modes at large D revisited, arXiv:1806.04888 [INSPIRE].
A. Sadhu and V. Suneeta, Study of semiclassical instability of the Schwarzschild AdS black hole in the large D limit, Class. Quant. Grav. 36 (2019) 115005 [arXiv:1812.11742] [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, JHEP 12 (2016) 113 [arXiv:1607.06475] [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].
S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [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, 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 Y. Dandekar, Black holes in presence of cosmological constant: second order in \( \frac{1}{D} \), JHEP 10 (2018) 171 [arXiv:1805.00284] [INSPIRE].
M. Mandlik and S. Thakur, Stationary solutions from the large D membrane paradigm, JHEP 11 (2018) 026 [arXiv:1806.04637] [INSPIRE].
A. Saha, The large D membrane paradigm for Einstein-Gauss-Bonnet gravity, JHEP 01 (2019) 028 [arXiv:1806.05201] [INSPIRE].
S. Kundu and P. Nandi, Large D gravity and charged membrane dynamics with nonzero cosmological constant, JHEP 12 (2018) 034 [arXiv:1806.08515] [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].
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].
P. Biswas, Stress tensor for large-D membrane at subleading orders, JHEP 07 (2020) 110 [arXiv:1912.00476] [INSPIRE].
M. Patra, Comparison between fluid-gravity and membrane-gravity dualities for Einstein-Maxwell system, arXiv:1912.09402 [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [INSPIRE].
H. Elvang, R. Emparan and A. Virmani, Dynamics and stability of black rings, JHEP 12 (2006) 074 [hep-th/0608076] [INSPIRE].
G.T. Horowitz and K. Maeda, Fate of the black string instability, Phys. Rev. Lett. 87 (2001) 131301 [hep-th/0105111] [INSPIRE].
P. Figueras, M. Kunesch and S. Tunyasuvunakool, End point of black ring instabilities and the weak cosmic censorship conjecture, Phys. Rev. Lett. 116 (2016) 071102 [arXiv:1512.04532] [INSPIRE].
H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].
H. Elvang, R. Emparan and P. Figueras, Phases of five-dimensional black holes, JHEP 05 (2007) 056 [hep-th/0702111] [INSPIRE].
H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.16163
Rights and permissions
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.
About this article
Cite this article
Mandlik, M. Black rings in large D membrane paradigm at the first order. J. High Energ. Phys. 2021, 36 (2021). https://doi.org/10.1007/JHEP02(2021)036
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)036