Advertisement

Hydrodynamics from charged black branes

  • Nabamita Banerjee
  • Jyotirmoy BhattacharyaEmail author
  • Sayantani Bhattacharyya
  • Suvankar Dutta
  • R. Loganayagam
  • P. Surówka
Open Access
Article

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.

Keywords

AdS-CFT Correspondence Black Holes Holography and quark-gluon plasmas 

References

  1. [1]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    S. Bhattacharyya et al., Local Fluid Dynamical Entropy from Gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [SPIRES].CrossRefADSGoogle Scholar
  3. [3]
    S. Bhattacharyya et al., Forced Fluid Dynamics from Gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    M. Van Raamsdonk, Black Hole Dynamics From Atmospheric Science, JHEP 05 (2008) 106 [arXiv:0802.3224] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    R. Loganayagam, Entropy Current in Conformal Hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    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].
  8. [8]
    S. Dutta, Higher Derivative Corrections to Locally Black Brane Metrics, JHEP 05 (2008) 082 [arXiv:0804.2453] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    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].CrossRefADSGoogle Scholar
  10. [10]
    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].MathSciNetADSGoogle Scholar
  11. [11]
    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].MathSciNetADSGoogle Scholar
  12. [12]
    S. Nakamura and S.-J. Sin, A holographic dual of hydrodynamics, JHEP 09 (2006) 020 [hep-th/0607123] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    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].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    R.A. Janik, Viscous plasma evolution from gravity using AdS/CFT, Phys. Rev. Lett. 98 (2007) 022302 [hep-th/0610144] [SPIRES].CrossRefADSGoogle Scholar
  15. [15]
    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].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    K. Kajantie and T. Tahkokallio, Spherically expanding matter in AdS/CFT, Phys. Rev. D 75 (2007) 066003 [hep-th/0612226] [SPIRES].MathSciNetADSGoogle Scholar
  17. [17]
    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].MathSciNetADSGoogle Scholar
  18. [18]
    C.P. Herzog, The hydrodynamics of M-theory, JHEP 12 (2002) 026 [hep-th/0210126] [SPIRES].CrossRefADSGoogle Scholar
  19. [19]
    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].CrossRefMathSciNetADSGoogle Scholar
  20. [20]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    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].CrossRefMathSciNetADSGoogle Scholar
  22. [22]
    C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    C.P. Herzog, The sound of M-theory, Phys. Rev. D 68 (2003) 024013 [hep-th/0302086] [SPIRES].ADSGoogle 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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    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].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    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].CrossRefADSGoogle Scholar
  29. [29]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].ADSGoogle Scholar
  30. [30]
    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].CrossRefMathSciNetADSGoogle Scholar
  31. [31]
    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].MathSciNetADSGoogle Scholar
  32. [32]
    J. Mas, Shear viscosity from R-charged AdS black holes, JHEP 03 (2006) 016 [hep-th/0601144] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    O. Saremi, The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical potential, JHEP 10 (2006) 083 [hep-th/0601159] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  34. [34]
    D.T. Son and A.O. Starinets, Hydrodynamics of R-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  35. [35]
    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].ADSGoogle Scholar
  36. [36]
    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].CrossRefADSGoogle Scholar
  37. [37]
    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].CrossRefADSGoogle Scholar
  38. [38]
    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].CrossRefADSGoogle Scholar
  39. [39]
    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].ADSGoogle Scholar
  40. [40]
    E.V. Shuryak, Strongly coupled quark-gluon plasma: The status report, hep-ph/0608177 [SPIRES].
  41. [41]
    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].CrossRefADSGoogle Scholar
  42. [42]
    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].CrossRefMathSciNetADSGoogle Scholar
  43. [43]
    M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  44. [44]
    V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  45. [45]
    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].CrossRefMathSciNetADSGoogle Scholar
  46. [46]
    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].ADSGoogle Scholar
  47. [47]
    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].CrossRefADSGoogle Scholar
  48. [48]
    M. Cvetič and S.S. Gubser, Thermodynamic Stability and Phases of General Spinning Branes, JHEP 07 (1999) 010 [hep-th/9903132] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    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].MathSciNetADSGoogle Scholar
  50. [50]
    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].MathSciNetADSGoogle Scholar
  51. [51]
    D. Astefanesei, N. Banerjee and S. Dutta, (Un)attractor black holes in higher derivative AdS gravity, JHEP 11 (2008) 070 [arXiv:0806.1334] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  52. [52]
    D. Astefanesei, H. Nastase, H. Yavartanoo and S. Yun, Moduli flow and non-supersymmetric AdS attractors, JHEP 04 (2008) 074 [arXiv:0711.0036] [SPIRES].CrossRefMathSciNetGoogle Scholar
  53. [53]
    R.-G. Cai and A. Wang, Thermodynamics and stability of hyperbolic charged black holes, Phys. Rev. D 70 (2004) 064013 [hep-th/0406057] [SPIRES].MathSciNetADSGoogle Scholar
  54. [54]
    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].ADSGoogle Scholar
  55. [55]
    M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].CrossRefADSGoogle Scholar
  56. [56]
    J.T. Liu and W.A. Sabra, Mass in anti-de Sitter spaces, Phys. Rev. D 72 (2005) 064021 [hep-th/0405171] [SPIRES].MathSciNetADSGoogle Scholar
  57. [57]
    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].CrossRefADSGoogle Scholar
  58. [58]
    S.S. Gubser, Thermodynamics of spinning D3-branes, Nucl. Phys. B 551 (1999) 667 [hep-th/9810225] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  59. [59]
    N. Banerjee and S. Dutta, Phase Transition of Electrically Charged Ricci-flat Black Holes, JHEP 07 (2007) 047 [arXiv:0705.2682] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  60. [60]
    D. Marolf, Chern-Simons terms and the three notions of charge, hep-th/0006117 [SPIRES].
  61. [61]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].CrossRefMathSciNetADSGoogle Scholar

Copyright information

© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Nabamita Banerjee
    • 1
  • Jyotirmoy Bhattacharya
    • 2
    Email author
  • Sayantani Bhattacharyya
    • 2
  • Suvankar Dutta
    • 1
  • R. Loganayagam
    • 2
  • P. Surówka
    • 3
    • 4
  1. 1.Harish-Chandra Research InstituteAllahabad-211019India
  2. 2.Dept. of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia
  3. 3.Department of PhysicsUniversity of WashingtonSeattleU.S.A.
  4. 4.Institute of PhysicsJagiellonian UniversityKrakówPoland

Personalised recommendations