Abstract
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
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S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-volume effective theory for higher-dimensional black holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
J. Camps and R. Emparan, Derivation of the blackfold effective theory, JHEP 03 (2012) 038 [Erratum ibid. 1206 (2012) 155] [arXiv:1201.3506] [INSPIRE].
J.D. Brown and J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [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].
J. Armas, J. Camps, T. Harmark and N.A. Obers, The Young modulus of black strings and the fine structure of blackfolds, JHEP 02 (2012) 110 [arXiv:1110.4835] [INSPIRE].
J. Armas, J. Gath and N.A. Obers, Black branes as piezoelectrics, Phys. Rev. Lett. 109 (2012) 241101 [arXiv:1209.2127] [INSPIRE].
J. Armas and N.A. Obers, Relativistic elasticity of stationary fluid branes, Phys. Rev. D 87 (2013) 044058 [arXiv:1210.5197] [INSPIRE].
M. Costa and G. Papadopoulos, Superstring dualities and p-brane bound states, Nucl. Phys. B 510 (1998) 217 [hep-th/9612204] [INSPIRE].
J. Breckenridge, G. Michaud and R.C. Myers, More D-brane bound states, Phys. Rev. D 55 (1997) 6438 [hep-th/9611174] [INSPIRE].
M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional rotating charged black holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].
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] [INSPIRE].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].
A. Buchel, Bulk viscosity of gauge theory plasma at strong coupling, Phys. Lett. B 663 (2008) 286 [arXiv:0708.3459] [INSPIRE].
B. Gouteraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].
M. Smolic, Holography and hydrodynamics for EMD theory with two Maxwell fields, JHEP 03 (2013) 124 [arXiv:1301.6020] [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].
T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav. 24 (2007) R1 [hep-th/0701022] [INSPIRE].
T. Harmark, V. Niarchos and N.A. Obers, Instabilities of near-extremal smeared branes and the correlated stability conjecture, JHEP 10 (2005) 045 [hep-th/0509011] [INSPIRE].
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] [INSPIRE].
D.T. Son and A.O. Starinets, Hydrodynamics of r-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [INSPIRE].
N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [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].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [INSPIRE].
J. Armas and N.A. Obers, Blackfolds in (Anti)-de Sitter backgrounds, Phys. Rev. D 83 (2011) 084039 [arXiv:1012.5081] [INSPIRE].
J. Armas, T. Harmark, N.A. Obers, M. Orselli and A.V. Pedersen, Thermal giant gravitons, JHEP 11 (2012) 123 [arXiv:1207.2789] [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].
S. Bhattacharyya, R. Loganayagam, I. Mandal, S. Minwalla and A. Sharma, Conformal nonlinear fluid dynamics from gravity in arbitrary dimensions, JHEP 12 (2008) 116 [arXiv:0809.4272] [INSPIRE].
G. Gibbons and K.-i. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds in supergravity and string theory, JHEP 08 (2011) 154 [arXiv:1106.4428] [INSPIRE].
P. Romatschke, Relativistic viscous fluid dynamics and non-equilibrium entropy, Class. Quant. Grav. 27 (2010) 025006 [arXiv:0906.4787] [INSPIRE].
L.D. Landau and E.M. Lifshitz, Fluid mechanics, 2nd edition, Course of Theoretical Physics volume 6, Pergamon Press, U.K. (1987).
S. Bhattacharyya et al., Local fluid dynamical entropy from gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
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Gath, J., Pedersen, A.V. Viscous asymptotically flat Reissner-Nordström black branes. J. High Energ. Phys. 2014, 59 (2014). https://doi.org/10.1007/JHEP03(2014)059
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DOI: https://doi.org/10.1007/JHEP03(2014)059