Abstract
We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].
S. Bhattacharyya et al., Local Fluid Dynamical Entropy from Gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [SPIRES].
S. Bhattacharyya et al., Forced Fluid Dynamics from Gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [SPIRES].
M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [SPIRES].
M. Van Raamsdonk, Black Hole Dynamics From Atmospheric Science, JHEP 05 (2008) 106 [arXiv:0802.3224] [SPIRES].
R. Loganayagam, Entropy Current in Conformal Hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [SPIRES].
M.P. Heller, P. Surowka, R. Loganayagam, M. Spalinski and S.E. Vazquez, On a consistent AdS/CFT description of boost-invariant plasma, arXiv:0805.3774 [SPIRES].
S. Dutta, Higher Derivative Corrections to Locally Black Brane Metrics, JHEP 05 (2008) 082 [arXiv:0804.2453] [SPIRES].
G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [SPIRES].
R.A. Janik and R.B. Peschanski, Asymptotic perfect fluid dynamics as a consequence of AdS/CFT, Phys. Rev. D 73 (2006) 045013 [hep-th/0512162] [SPIRES].
R.A. Janik and R.B. Peschanski, Gauge/gravity duality and thermalization of a boost-invariant perfect fluid, Phys. Rev. D 74 (2006) 046007 [hep-th/0606149] [SPIRES].
S. Nakamura and S.-J. Sin, A holographic dual of hydrodynamics, JHEP 09 (2006) 020 [hep-th/0607123] [SPIRES].
S.-J. Sin, S. Nakamura and S.P. Kim, Elliptic Flow, Kasner Universe and Holographic Dual of RHIC Fireball, JHEP 12 (2006) 075 [hep-th/0610113] [SPIRES].
R.A. Janik, Viscous plasma evolution from gravity using AdS/CFT, Phys. Rev. Lett. 98 (2007) 022302 [hep-th/0610144] [SPIRES].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. P ufu, Expanding plasmas and quasinormal modes of anti-de Sitter black holes, JHEP 04 (2007) 080 [hep-th/0611005] [SPIRES].
K. Kajantie and T. Tahkokallio, Spherically expanding matter in AdS/CFT, Phys. Rev. D 75 (2007) 066003 [hep-th/0612226] [SPIRES].
P. Benincasa, A. Buchel, M.P. Heller and R.A. Janik, On the supergravity description of boost invariant conformal plasma at strong coupling, Phys. Rev. D 77 (2008) 046006 [arXiv:0712.2025] [SPIRES].
C.P. Herzog, The hydrodynamics of M-theory, JHEP 12 (2002) 026 [hep-th/0210126] [SPIRES].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. II: Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [SPIRES].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES].
C.P. Herzog, The sound of M-theory, Phys. Rev. D 68 (2003) 024013 [hep-th/0302086] [SPIRES].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [SPIRES].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES].
A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [hep-th/0406264] [SPIRES].
A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [SPIRES].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [SPIRES].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].
P. Benincasa, A. Buchel and A.O. Starinets, Sound waves in strongly coupled non-conformal gauge theory plasma, Nucl. Phys. B 733 (2006) 160 [hep-th/0507026] [SPIRES].
K. Maeda, M. Natsuume and T. Okamura, Viscosity of gauge theory plasma with a chemical potential from AdS/CFT, Phys. Rev. D 73 (2006) 066013 [hep-th/0602010] [SPIRES].
J. Mas, Shear viscosity from R-charged AdS black holes, JHEP 03 (2006) 016 [hep-th/0601144] [SPIRES].
O. Saremi, The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical potential, JHEP 10 (2006) 083 [hep-th/0601159] [SPIRES].
D.T. Son and A.O. Starinets, Hydrodynamics of R-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [SPIRES].
P. Benincasa, A. Buchel and R. Naryshkin, The shear viscosity of gauge theory plasma with chemical potentials, Phys. Lett. B 645 (2007) 309 [hep-th/0610145] [SPIRES].
K.B. Fadafan, Charge effect and finite ’t Hooft coupling correction on drag force and Jet Quenching Parameter, Eur. Phys. J. C 68 (2010) 505 [arXiv:0809.1336] [SPIRES].
D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].
E. Shuryak, Why does the quark gluon plasma at RHIC behave as a nearly ideal fluid?, Prog. Part. Nucl. Phys. 53 (2004) 273 [hep-ph/0312227] [SPIRES].
E.V. Shuryak, What RHIC experiments and theory tell us about properties of quark-gluon plasma?, Nucl. Phys. A 750 (2005) 64 [hep-ph/0405066] [SPIRES].
E.V. Shuryak, Strongly coupled quark-gluon plasma: The status report, hep-ph/0608177 [SPIRES].
J.-L. Gervais and B. Sakita, Quantized relativistic string as a strong coupling limit of the Higgs model, Nucl. Phys. B 91 (1975) 301 [SPIRES].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [SPIRES].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [SPIRES].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].
S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla, Large rotating AdS black holes from fluid mechanics, JHEP 09 (2008) 054 [arXiv:0708.1770] [SPIRES].
A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at finite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837] [SPIRES].
A. Buchel and M. Paulos, Second order hydrodynamics of a CFT plasma from boost invariant expansion, Nucl. Phys. B 810 (2009) 40 [arXiv:0808.1601] [SPIRES].
M. Cvetič and S.S. Gubser, Thermodynamic Stability and Phases of General Spinning Branes, JHEP 07 (1999) 010 [hep-th/9903132] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [SPIRES].
D. Astefanesei, N. Banerjee and S. Dutta, (Un)attractor black holes in higher derivative AdS gravity, JHEP 11 (2008) 070 [arXiv:0806.1334] [SPIRES].
D. Astefanesei, H. Nastase, H. Yavartanoo and S. Yun, Moduli flow and non-supersymmetric AdS attractors, JHEP 04 (2008) 074 [arXiv:0711.0036] [SPIRES].
R.-G. Cai and A. Wang, Thermodynamics and stability of hyperbolic charged black holes, Phys. Rev. D 70 (2004) 064013 [hep-th/0406057] [SPIRES].
R.-G. Cai and K.-S. Soh, Critical behavior in the rotating D-branes, Mod. Phys. Lett. A 14 (1999) 1895 [hep-th/9812121] [SPIRES].
M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].
J.T. Liu and W.A. Sabra, Mass in anti-de Sitter spaces, Phys. Rev. D 72 (2005) 064021 [hep-th/0405171] [SPIRES].
M. Cvetič and S.S. Gubser, Phases of R-charged black holes, spinning branes and strongly coupled gauge theories, JHEP 04 (1999) 024 [hep-th/9902195] [SPIRES].
S.S. Gubser, Thermodynamics of spinning D3-branes, Nucl. Phys. B 551 (1999) 667 [hep-th/9810225] [SPIRES].
N. Banerjee and S. Dutta, Phase Transition of Electrically Charged Ricci-flat Black Holes, JHEP 07 (2007) 047 [arXiv:0705.2682] [SPIRES].
D. Marolf, Chern-Simons terms and the three notions of charge, hep-th/0006117 [SPIRES].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0809.2596
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Banerjee, N., Bhattacharya, J., Bhattacharyya, S. et al. Hydrodynamics from charged black branes. J. High Energ. Phys. 2011, 94 (2011). https://doi.org/10.1007/JHEP01(2011)094
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2011)094