Probing the hydrodynamic limit of (super)gravity

  • Adriana Di Dato
  • Jakob Gath
  • Andreas Vigand Pedersen
Open Access
Regular Article - Theoretical Physics


We study the long-wavelength effective description of two general classes of charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes in ten and eleven dimensional supergravity. In particular, we consider gravitational brane solutions in a hydrodynamic derivative expansion (to first order) for arbitrary dilaton coupling and for general brane and co-dimension and determine their effective electro-fluid-dynamic descriptions by exacting the characterizing transport coefficients. We also investigate the stability properties of the corresponding hydrodynamic systems by analyzing their response to small long-wavelength perturbations. For branes carrying unsmeared charge, we find that in a certain regime of parameter space there exists a branch of stable charged configurations. This is in accordance with the expectation that D/NS/M-branes have stable configurations, except for the D5, D6, and NS5. In contrast, we find that Maxwell charged brane configurations are Gregory-Laflamme unstable independently of the charge and, in particular, verify that smeared configurations of D0-branes are unstable. Finally, we provide a modification to the mapping presented in arXiv:1211.2815 and utilize it to provide a non-trivial cross-check on a certain subset of our transport coefficients with the results of arXiv:1110.2320.


p-branes Black Holes in String Theory D-branes AdS-CFT Correspondence 


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.


  1. [1]
    J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    T. Damour, Black hole Eddy currents, Phys. Rev. D 18 (1978) 3598 [INSPIRE].ADSGoogle Scholar
  4. [4]
    R.H. Price and K.S. Thorne, Membrane viewpoint on black holes: properties and evolution of the stretched horizon, Phys. Rev. D 33 (1986) 915 [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    L.D. Landau and E.M. Lifshitz, Fluid mechanics, 2nd edition, Course of theoretical physics volume 6. Pergamon Press, London (1987).Google Scholar
  7. [7]
    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].ADSCrossRefGoogle Scholar
  8. [8]
    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].ADSMathSciNetGoogle Scholar
  9. [9]
    D.T. Son and A.O. Starinets, Hydrodynamics of r-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  11. [11]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    S. Bhattacharyya et al., Forced fluid dynamics from gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  14. [14]
    J. Gath and A.V. Pedersen, Viscous asymptotically flat Reissner-Nordström black branes, JHEP 03 (2014) 059 [arXiv:1302.5480] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav. 24 (2007) R1 [hep-th/0701022] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    B. Kol, Topology change in general relativity and the black hole black string transition, JHEP 10 (2005) 049 [hep-th/0206220] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds in supergravity and string theory, JHEP 08 (2011) 154 [arXiv:1106.4428] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    H.S. Reall, Classical and thermodynamic stability of black branes, Phys. Rev. D 64 (2001) 044005 [hep-th/0104071] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    P. Bostock and S.F. Ross, Smeared branes and the Gubser-Mitra conjecture, Phys. Rev. D 70 (2004) 064014 [hep-th/0405026] [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, Black hole-black string phase transitions in thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle, Class. Quant. Grav. 21 (2004) 5169 [hep-th/0406210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    A. Buchel, Bulk viscosity of gauge theory plasma at strong coupling, Phys. Lett. B 663 (2008) 286 [arXiv:0708.3459] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    R. Emparan, V.E. Hubeny and M. Rangamani, Effective hydrodynamics of black D3-branes, JHEP 06 (2013) 035 [arXiv:1303.3563] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    I. Bredberg, C. Keeler, V. Lysov and A. Strominger, From Navier-Stokes to Einstein, JHEP 07 (2012) 146 [arXiv:1101.2451] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    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].ADSGoogle Scholar
  32. [32]
    M.M. Caldarelli, J. Camps, B. Goutéraux and K. Skenderis, AdS/Ricci-flat correspondence, JHEP 04 (2014) 071 [arXiv:1312.7874] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    R. Argurio, F. Englert and L. Houart, Intersection rules for p-branes, Phys. Lett. B 398 (1997) 61 [hep-th/9701042] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    R. Argurio, Intersection rules and open branes, hep-th/9712170 [INSPIRE].
  37. [37]
    A.W. Peet, TASI lectures on black holes in string theory, hep-th/0008241 [INSPIRE].
  38. [38]
    M. Huq and M.A. Namazie, Kaluza-Klein supergravity in ten-dimensions, Class. Quant. Grav. 2 (1985) 293 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    F. Giani and M. Pernici, N = 2 supergravity in ten-dimensions, Phys. Rev. D 30 (1984) 325 [INSPIRE].ADSMathSciNetGoogle Scholar
  40. [40]
    I. Campbell and P. West, N = 2, d = 10 non-chiral supergravity and its spontaneous compactification, Nucl. Phys. B 243 (1984) 112.ADSCrossRefGoogle Scholar
  41. [41]
    E. Cremmer, B. Julia and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    A.A. Tseytlin, Composite black holes in string theory, gr-qc/9608044 [INSPIRE].
  43. [43]
    M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional rotating charged black holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  45. [45]
    R. Emparan, Blackfolds, arXiv:1106.2021 [INSPIRE].
  46. [46]
    S.S. Gubser and I. Mitra, Instability of charged black holes in anti-de Sitter space, hep-th/0009126 [INSPIRE].
  47. [47]
    S.S. Gubser and I. Mitra, The evolution of unstable black holes in Anti-de Sitter space, JHEP 08 (2001) 018 [hep-th/0011127] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    S.F. Ross and T. Wiseman, Smeared D0 charge and the Gubser-Mitra conjecture, Class. Quant. Grav. 22 (2005) 2933 [hep-th/0503152] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  49. [49]
    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].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  51. [51]
    I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    R. Gregory, Black string instabilities in Anti-de Sitter space, Class. Quant. Grav. 17 (2000) L125 [hep-th/0004101] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  53. [53]
    A. Buchel, Violation of the holographic bulk viscosity bound, Phys. Rev. D 85 (2012) 066004 [arXiv:1110.0063] [INSPIRE].ADSMathSciNetGoogle Scholar
  54. [54]
    A. Di Dato, Kaluza-Klein reduction of relativistic fluids and their gravity duals, JHEP 12 (2013) 087 [arXiv:1307.8365] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  55. [55]
    T. Hirayama, G. Kang and Y. Lee, Classical stability of charged black branes and the Gubser-Mitra conjecture, Phys. Rev. D 67 (2003) 024007 [hep-th/0209181] [INSPIRE].ADSMathSciNetGoogle Scholar
  56. [56]
    J. Erdmenger, M. Rangamani, S. Steinfurt and H. Zeller, Hydrodynamic Regimes of Spinning Black D3-branes, JHEP 02 (2015) 026 [arXiv:1412.0020] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    J. Gath and A.V. Pedersen, work in progress.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Adriana Di Dato
    • 1
  • Jakob Gath
    • 2
  • Andreas Vigand Pedersen
    • 3
    • 4
  1. 1.Departament de Física Fonamental, Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  2. 2.Centre de Physique ThéoriqueEcole Polytechnique, CNRS UMR 7644Palaiseau CedexFrance
  3. 3.Center for Theoretical Physics and Department of PhysicsUniversity of CaliforniaBerkeleyUnited States
  4. 4.Niels Bohr InstituteUniversity of CopenhagenCopenhagen ØDenmark

Personalised recommendations