Gravity and hydrodynamics: Lectures on the fluid-gravity correspondence

Classical and Quantum Gravity

Volumn 26, Issue 22, 2009, Pages

  Rangamani, Mukund ^a,b  

^a DURHAM UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449698220     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/26/22/224003     Document Type: Article

References (123)

1. Maldacena J M 1998 The large nlimit of superconformal field theories and supergravity Adv. Theor. Math. Phys. 2 231-52 (arXiv:hep-th/9711200)
2. Gubser S S, Klebanov I R and Polyakov A M 1998 Gauge theory correlators from non-critical string theory Phys. Lett. B 428 105-114 (arXiv:hep-th/9802109)
3. Witten E 1998 Anti-de sitter space and holography Adv. Theor. Math. Phys. 2 253-91 (arXiv:hep-th/9802150)
4. Bhattacharyya S, Hubeny V E, Minwalla S and Rangamani M 2007 Nonlinear fluid dynamics from gravity arXiv:0712.2456
5. Fefferman C 2000 Existence and smoothness of the Navier-Stokes equation Clay Millenium Problems
6. Emparan R and Reall H S 2008 Black holes in higher dimensions arXiv:0801.3471
7. Gregory R and Laflamme R 1993 Black strings and p-branes are unstable Phys. Rev. Lett. 70 2837-40 (arXiv:hep-th/9301052)
8. Emparan R and Myers R C 2003 Instability of ultra-spinning black holes J. High Energy Phys. JHEP09(2003)025 (arXiv:hep-th/0308056)
9. Thorne K, Macdonald D and Price R 1986 Black Holes: The Membrane Paradigm (New Haven, CT: Yale University Press)
10. Damour T and Lilley M 2008 String theory, gravity and experiment arXiv:0802.4169
11. Cardoso V and Dias O J C 2006 Gregory-Laflamme and Rayleigh-Plateau instabilities Phys. Rev. Lett. 96 181601 (arXiv:hep-th/0602017)
12. Lahiri S and Minwalla S 2007 Plasmarings as dual black rings arXiv:0705.3400 [hep-th]
13. Bhardwaj S and Bhattacharya J 2008 thermodynamics of plasmaballs and plasmarings in 3+1 dimensions arXiv:0806.1897
14. Bhattacharya J and Lahiri S 2009 Lumps of plasma in arbitrary dimensions arXiv:0903.4734
15. Caldarelli M M, Dias O J C, Emparan R and Klemm D 2008 Black holes as lumps of fluid arXiv:0811.2381
16. Maeda K-i and Miyamoto U 2008 Black hole-black string phase transitions from hydrodynamics arXiv:0811.2305
17. Aarts G 2009 Two complex problems on the lattice: transport coefficients and finite chemical potential Nucl. Phys. A 820 57c-64c (arXiv:0811.1850)
18. Gubser S S, Klebanov I R and Peet A W 1996 Entropy and temperature of black 3-branes Phys. Rev. D 54 3915-19 (arXiv:hep-th/9602135)
19. Kovtun P, Son D T and Starinets A O 2005 Viscosity in strongly interacting quantum field theories from black hole physics Phys. Rev. Lett. 94 111601 (arXiv:hep-th/0405231)
20. Shuryak E 2004 Why does the quark gluon plasma at rhic behave as a nearly ideal fluid? Prog. Part. Nucl. Phys. 53 273-303 (arXiv:hep-ph/0312227)
21. Shuryak E V 2005 What RHIC experiments and theory tell us about properties of quark-gluon plasma? Nucl. Phys. A 750 64-83 (arXiv:hep-ph/0405066)
22. Shuryak E V 2006 Strongly coupled quark-gluon plasma: the status report arXiv:hep-ph/0608177
23. Shuryak E 2009 Physics of Strongly coupled Quark-Gluon Plasma Prog. Part. Nucl. Phys. 62 48-101 (arXiv:0807.3033)
24. Schaefer T and Teaney D 2009 nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas arXiv:0904.3107
25. Horowitz G T and Hubeny V E 2000 Quasinormal modes of AdS black holes and the approach to thermal equilibrium Phys. Rev. D 62 024027 (arXiv:hep-th/ 9909056)
26. Policastro G, Son D T and Starinets A O 2001 The shear viscosity of strongly coupled n = 4 supersymmetric Yang-Mills plasma Phys. Rev. Lett. 87 081601 (arXiv:hep-th/0104066)
27. Herzog C P 2002 The hydrodynamics of m-theory J. High Energy Phys. JHEP12(2002)026 (arXiv:hep-th/0210126)
28. Policastro G, Son D T and Starinets A O 2002 From ADS/CFT correspondence to hydrodynamics: ii. Sound waves J. High Energy Phys. JHEP12(2002)054 (arXiv:hep-th/0210220)
29. Policastro G, Son D T and Starinets A O 2002 From ADS/CFT correspondence to hydrodynamics J. High Energy Phys. JHEP09(2002)043 (arXiv:hep-th/0205052)
30. Son D T and Starinets A O 2002 Minkowski-space correlators in ADS/CFT correspondence: recipe and applications J. High Energy Phys. JHEP09(2002)042 (arXiv:hep-th/0205051)
31. Herzog C P and Son D T 2002 Schwinger-Keldysh propagators from ADS/CFT correspondence J. High Energy Phys. JHEP03(2003)046 (arXiv:hep-th/0212072)
32. Herzog C P 2003 The sound of m-theory Phys. Rev. D 68 024013 (arXiv:hep-th/0302086)
33. Kovtun P, Son D T and Starinets A O 2003 Holography and hydrodynamics: diffusion on stretched horizons J. High Energy Phys. JHEP10(2003)064 (arXiv:hep-th/0309213)
34. Buchel A and Liu J T 2004 Universality of the shear viscosity in supergravity Phys. Rev. Lett. 93 090602 (arXiv:hep-th/0311175)
35. Buchel A, Liu J T and Starinets A O 2005 Coupling constant dependence of the shear viscosity in n = 4 supersymmetric Yang-Mills theory Nucl. Phys. B 707 56-68 (arXiv:hep-th/0406264)
36. Buchel A 2005 On universality of stress-energy tensor correlation functions in supergravity Phys. Lett. B 609 392-401 (arXiv:hep-th/0408095)
37. Kovtun P K and Starinets A O 2005 Quasinormal modes and holography Phys. Rev. D 72 086009 (arXiv:hep-th/0506184)
38. Benincasa P, Buchel A and Starinets A O 2006 Sound waves in strongly coupled non-conformal gauge theory plasma Nucl. Phys. B 733 160-87 (arXiv:hep-th/0507026)
39. Maeda K, Natsuume M and Okamura T 2006 Viscosity of gauge theory plasma with a chemical potential from ADS/CFT Phys. Rev. D 73 066013 (arXiv:hep-th/0602010)
40. Mas J 2006 Shear viscosity from r-charged AdS black holes J. High Energy Phys. JHEP03(2006)016 (arXiv:hep-th/0601144)
41. Saremi O 2006 The viscosity bound conjecture and hydrodynamics of m2-brane theory at finite chemical potential J. High Energy Phys. JHEP10(2006)083 (arXiv:hep-th/0601159)
42. Son D T and Starinets A O 2006 Hydrodynamics of r-charged black holes J. High Energy Phys. JHEP03(2006)052 (arXiv:hep-th/0601157)
43. Benincasa P, Buchel A and Naryshkin R 2007 The shear viscosity of gauge theory plasma with chemical potentials Phys. Lett. B 645 309-13 (arXiv:hep-th/0610145)
44. Myers R C, Paulos M F and Sinha A 2009 Phys. Rev. D 79 041901 (arXiv:0806.2156)
45. Garousi M R and Ghodsi A 2009 Nucl. Phys. B 812 470 (arXiv:0808.0411)
46. Ghodsi A and Alishahiha M Non-relativistic D3-brane in the presence of higher derivative corrections arXiv:0901.3481
47. Son D T and Starinets A O 2007 Viscosity, black holes and quantum field theory arXiv:0704.024 [hep-th]
48. Janik R A and Peschanski R 2006 Asymptotic perfect fluid dynamics as a consequence of ADS/CFT Phys. Rev. D 73 045013 (arXiv:hep-th/0512162)
49. Janik R A and Peschanski R 2006 Gauge/gravity duality and thermalization of a boost-invariant perfect fluid Phys. Rev. D 74 046007 (arXiv:hep-th/0606149)
50. Nakamura S and Sin S-J 2006 A holographic dual of hydrodynamics J. High Energy Phys. JHEP09(2006)020 (arXiv:hep-th/0607123)
51. Sin S-J, Nakamura S and Kim S P 2006 Elliptic flow, Kasner universe and holographic dual of RHIC fireball J. High Energy Phys. JHEP12(2006)075 (arXiv:hep-th/0610113)
52. Janik R A 2007 Viscous plasma evolution from gravity using ADS/CFT Phys. Rev. Lett. 98 022302 (arXiv:hep-th/0610144)
53. Friess J J, Gubser S S, Michalogiorgakis G and Pufu S S 2007 Expanding plasmas and quasinormal modes of anti-de sitter black holes J. High Energy Phys. JHEP04(2007)080 (arXiv:hep-th/0611005)
54. Kajantie K and Tahkokallio T 2007 Spherically expanding matter in ads/cft Phys. Rev. D 75 066003 (arXiv:hep-th/0612226)
55. Heller M P and Janik R A 2007 Viscous hydrodynamics relaxation time from ads/cft Phys. Rev. D 76 025027 (arXiv:hep-th/0703243)
56. Kajantie K, Louko J and Tahkokallio T 2007 Gravity dual of (1+1)-dimensional Bjorken expansion Phys. Rev. D 76 106006 arXiv:0705.179 [hep-th]
57. Benincasa P, Buchel A, Heller M P and Janik R A 2007 On the supergravity description of boost invariant conformal plasma at strong coupling (arXiv:0712.2025 [hep-th])
58. Natsuume M and Okamura T 2008 Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality Phys. Rev. D 77 066014 (arXiv:0712.2916)
59. Natsuume M and Okamura T 2008 A note on causal hydrodynamics for M-theory branes Prog. Theor. Phys. 120 1217-22 (arXiv:0801.1797)
60. Heller M P, Janik R A and Peschanski R 2008 Hydrodynamic flow of the quark-gluon plasma and gauge/gravity correspondence arXiv:0811.3113
61. Heller M P, Loganayagam R, Spalinski M, Surowka P and Vazquez S E 2008 On a consistent AdS/CFT description of boost-invariant plasma arXiv:0805.3774
62. Kinoshita S, Mukohyama S, Nakamura S and Oda K-y 2008 A holographic dual of Bjorken flow arXiv:0807.3797
63. Figueras P, Hubeny V E, Rangamani M and Ross S F 2009 Dynamical black holes and expanding plasmas arXiv:0902.4696
64. Bjorken J D 1983 Highly relativistic nucleus-nucleus collisions: the central rapidity region Phys. Rev. D 27 140-51
65. Bhattacharyya S, Lahiri S, Loganayagam R and Minwalla S 2007 Large rotating AdS black holes from fluid mechanics arXiv:0708.177 [hep-th]
66. Bhattacharyya S, Hubeny V E, Loganayagam R, Mandal G, Minwalla S, Morita T, Rangamani M and Reall H S 2008 Local fluid dynamical entropy from gravity arXiv:0803.2526
67. Van Raamsdonk M 2008 Black hole dynamics from atmospheric science J. High Energy Phys. JHEP05(2008)106 (arXiv:0802.3224)
68. Haack M and Yarom A 2008 Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT J. High Energy Phys. JHEP10(2008)063 (arXiv:0806.4602)
69. Bhattacharyya S, Loganayagam R, Mandal I, Minwalla S and Sharma A 2008 Conformal nonlinear fluid dynamics from gravity in arbitrary dimensions arXiv:0809.4272
70. Bhattacharyya S, Loganayagam R, Minwalla S, Nampuri S, Trivedi S P and Wadia S R 2008 Forced fluid dynamics from gravity arXiv:0806.0006
71. Erdmenger J, Haack M, Kaminski M and Yarom A 2008 Fluid dynamics of R-charged black holes arXiv:0809.2488
72. Banerjee N, Bhattacharya J, Bhattacharyya S, Dutta S, Loganayagam R and Surowka P 2008 Hydrodynamics from charged black branes arXiv:0809.2596
73. Hur J, Kim K K and Sin S-J 2009 Hydrodynamics with conserved current from the gravity dual J. High Energy Phys. JHEP03(2009)036 (arXiv:0809.4541)
74. Torabian M and Yee H-U 2009 Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries arXiv:0903.4894
75. Hansen J and Kraus P 2009 Nonlinear magnetohydrodynamics from gravity J. High Energy Phys. JHEP04(2009)048 (arXiv:0811.3468)
76. Caldarelli M M, Dias O J C and Klemm D 2008 Dyonic AdS black holes from magnetohydrodynamics J. High Energy Phys. JHEP03(2009)025 (arXiv:0812.0801)
77. Kanitscheider I and Skenderis K 2009 Universal hydrodynamics of non-conformal branes J. High Energy Phys. JHEP04(2009)062 (arXiv:0901.1487)
78. David J R, Mahato M and Wadia S R 2009 Hydrodynamics from the D1-brane J. High Energy Phys. JHEP04(2009)042 (arXiv:0901.2013)
79. Dutta S 2008 higher derivative corrections to locally black brane metrics arXiv:0804.2453
80. Rangamani M, Ross S F, Son D T and Thompson E G 2008 Conformal non-relativistic hydrodynamics from gravity arXiv:0811.2049
81. Bhattacharyya S, Minwalla S and Wadia S R 2008 The incompressible non-relativistic Navier-Stokes equation from gravity arXiv:0810.1545
82. Ambrosetti N, Charbonneau J and Weinfurtner S 2008 The fluid/gravity correspondence: lecture notes from the 2008 Summer School on particles, fields, and strings arXiv:0810.2631
83. Baier R, Romatschke P, Son D T, Starinets A O and Stephanov M A 2007 Relativistic viscous hydrodynamics, conformal invariance, and holography arXiv:0712.2451
84. Loganayagam R 2008 Entropy current in conformal hydrodynamics arXiv:0801.3701
85. Landau L and Lifshitz E 1965 Fluid Mechanics: Course of Theoretical Physics vol 6 (Oxford: Butterworth Heinemann)
86. Andersson N and Comer G L 2005 Relativistic fluid dynamics: Physics for many different scales Living Rev. Rel. 10 1
87. Israel W 1976 Nonstationary irreversible thermodynamics: a causal relativistic theory Ann. Phys. 100 310-31
88. Israel W and Stewart J M 1979 Transient relativistic thermodynamics and kinetic theory Ann. Phys. 118 341-72
89. Arnold P, Moore G D and Yaffe L G 2000 Transport coefficients in high temperature gauge theories: (I). Leading-log results J. High Energy Phys. JHEP11(2000)001 (arXiv:hep-ph/0010177)
90. Arnold P, Moore G D and Yaffe L G 2003 Transport coefficients in high temperature gauge theories: II. Beyond leading log J. High Energy Phys. JHEP05(2003)051 (arXiv:hep-ph/0302165)
91. Muronga A 2004 Causal theories of dissipative relativistic fluid dynamics for nuclear collisions Phys. Rev. C 69 034903 (arXiv:nucl-th/0309055)
92. Romatschke P 2009 New developments in relativistic viscous hydrodynamics arXiv:0902.3663
93. Geroch R P 2001 On hyperbolic 'Theories' of relativistic dissipative fluids arXiv:gr-qc/0103112
94. Wald R 1984 General Relativity (Chicago: University of Chicago Press) p 504
95. Henningson M and Skenderis K 1998 The holographic Weyl anomaly J. High Energy Phys. JHEP07(1998)023 (arXiv:hep-th/9806087)
96. Balasubramanian V and Kraus P 1999 A stress tensor for anti-de sitter gravity Commun. Math. Phys. 208 413-28 (arXiv:hep-th/9902121)
97. Sondow J and Weisstein E W 2009 Harmonic number MathWorld-A Wolfram Web Resource (05, 2009)
98. Witten E 1998 Anti-de sitter space, thermal phase transition and confinement in gauge theories Adv. Theor. Math. Phys. 2 505-32 (arXiv:hep-th/9803131)
99. de Haro S, Solodukhin S N and Skenderis K 2001 Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence Commun. Math. Phys. 217 595-622 (arXiv:hep-th/0002230)
100. Gupta R K and Mukhopadhyay A 2008 On the universal hydrodynamics of strongly coupled CFTs with gravity duals arXiv:0810.4851
101. Chesler P M and Yaffe L G 2008 Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma arXiv:0812.2053
102. Hubeny V E, Rangamani M and Takayanagi T 2007 A covariant holographic entanglement entropy proposal J. High Energy Phys. JHEP07(2007)062 arXiv:0705.0016
103. Hartnoll S A, Herzog C P and Horowitz G T 2008 Holographic superconductors arXiv:0810.1563
104. Herzog C P, Kovtun P K and Son D T 2008 Holographic model of superfluidity arXiv:0809.4870
105. Yarom A 2009 Fourth sound of holographic superfluids arXiv:0903.1353
106. Basu P, Mukherjee A and Shieh H H 2008 Supercurrent: vector Hair for an Ads black hole arXiv:0809.4494
107. Hubeny V E and Rangamani M unpublished
108. Haack M and Yarom A 2008 Universality of second order transport coefficients from the gauge-string duality arXiv:0811.1794
109. Herzog C P, Rangamani M and Ross S F 2008 Heating up Galilean holography arXiv:0807.1099
110. Adams A, Balasubramanian K and McGreevy J 2008 Hot spacetimes for cold atoms arXiv:0807.1111
111. Son D T 2008 Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry arXiv:0804.3972
112. Balasubramanian K and McGreevy J 2008 Gravity duals for non-relativistic CFTs arXiv:0804.4053
113. Maldacena J, Martelli D and Tachikawa Y 2008 Comments on string theory backgrounds with non-relativistic conformal symmetry arXiv:0807.1100
114. Gimon E G, Hashimoto A, Hubeny V E, Lunin O and Rangamani M 2003 Black strings in asymptotically plane wave geometries J. High Energy Phys. JHEP08(2003)035 (arXiv:hep-th/0306131)
115. Fouxon I and Oz Y 2008 Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations arXiv:0809.4512
116. Fouxon I and Oz Y 2008 CFT hydrodynamics: symmetries, exact solutions and gravity arXiv:0812.1266
117. Bagchi A and Gopakumar R 2009 Galilean conformal algebras and AdS/CFT arXiv:0902.1385
118. Gusyatnikova V N and Yumaguzhin V A 1989 Acta. Appl. Math. 15 65-81
119. Hassaine M and Horvthy P A 2000 Ann. Phys. (NY) 282 218
120. Hubeny V E, Rangamani M, Minwalla S and Van Raamsdonk M 2009 The fluid-gravity correspondence: the membrane at the end of the universe Int. J. Mod. Phys. D 17 2571-6
121. Eling C, Fouxon I and Oz Y 2009 The Incompressible Navier-Stokes equations from membrane dynamics arXiv:0905.3638
122. Iqbal N and Liu H 2009 Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm Phys. Rev. D 79 025023 (arXiv:0809.3808)
123. Bhattacharyya S and Minwalla S 2009 Weak field black hole formation in asymptotically AdS spacetimes arXiv:0904.0464