Abstract
We consider the fluid dual of (d + 2)-dimensional vacuum Einstein equation either with or without a cosmological constant. The background solutions admit black hole event horizons and the spatial sections of the horizons are conformally flat. Therefore, a d-dimensional flat Euclidean space \( {\mathbb{E}}^d \) is contained in the conformal class of the spatial section of the black hole horizon. A compressible, forced, stationary and viscous fluid system can be constructed on the product (Newtonian) spacetime \( \mathbb{R}\times {\mathbb{E}}^d \) as the lowest order fluctuation modes around such black hole background. This construction provides the first example of holographic duality which is beyond the class of bulk/boundary correspondence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, Dimensional reduction in quantum gravity, in proceedings of Salamfest, Trieste Italy (1993), pg. 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
T. Damour, Black Hole Eddy Currents, Phys. Rev. D 18 (1978) 3598 [INSPIRE].
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].
T. Damour and M. Lilley, String theory, gravity and experiment, arXiv:0802.4169 [INSPIRE].
C. Eling and Y. Oz, Relativistic CFT hydrodynamics from the membrane paradigm, JHEP 02 (2010) 069 [arXiv:0906.4999] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
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] [INSPIRE].
M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [INSPIRE].
S. Bhattacharyya et al., Forced Fluid Dynamics from Gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [INSPIRE].
S. Bhattacharyya, S. Minwalla and S.R. Wadia, The incompressible non-relativistic Navier-Stokes equation from gravity, JHEP 08 (2009) 059 [arXiv:0810.1545] [INSPIRE].
T. Ashok, Forced fluid dynamics from gravity in arbitrary dimensions, JHEP 03 (2014) 138 [arXiv:1309.6325] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled \( \mathcal{N}=4 \) supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
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] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian Approach to Fluid/Gravity Duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].
I. Bredberg, C. Keeler, V. Lysov and A. Strominger, From Navier-Stokes To Einstein, JHEP 07 (2012) 146 [arXiv:1101.2451] [INSPIRE].
G. Compere, P. McFadden, K. Skenderis and M. Taylor, The holographic fluid dual to vacuum Einstein gravity, JHEP 07 (2011) 050 [arXiv:1103.3022] [INSPIRE].
R.-G. Cai, L. Li and Y.-L. Zhang, Non-relativistic fluid dual to asymptotically AdS gravity at finite cutoff surface, JHEP 07 (2011) 027 [arXiv:1104.3281] [INSPIRE].
C. Eling, A. Meyer and Y. Oz, The relativistic rindler hydrodynamics, JHEP 05 (2012) 116 [arXiv:1201.2705] [INSPIRE].
G. Compere, P. McFadden, K. Skenderis and M. Taylor, The relativistic fluid dual to vacuum Einstein gravity, JHEP 03 (2012) 076 [arXiv:1201.2678] [INSPIRE].
G. Chirco, C. Eling and S. Liberati, Higher curvature gravity and the holographic fluid dual to flat spacetime, JHEP 08 (2011) 009 [arXiv:1105.4482] [INSPIRE].
X. Bai, Y.-P. Hu, B.-H. Lee and Y.-L. Zhang, Holographic charged fluid with anomalous current at finite cutoff surface in Einstein-Maxwell gravity, JHEP 11 (2012) 054 [arXiv:1207.5309] [INSPIRE].
D.-C. Zou, S.-J. Zhang and B. Wang, Holographic charged fluid dual to third order Lovelock gravity, Phys. Rev. D 87 (2013) 084032 [arXiv:1302.0904] [INSPIRE].
N. Banerjee et al., Constraints on fluid dynamics from equilibrium partition functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
Y.-P. Hu and J.-H. Zhang, Gravity/Fluid Correspondence and Its Application on Bulk Gravity with U(1) Gauge Field, Adv. High Energy Phys. 2014 (2014) 483814 [arXiv:1311.3974] [INSPIRE].
C. Niu, Y. Tian, X.-N. Wu and Y. Ling, Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories, Phys. Lett. B 711 (2012) 411 [arXiv:1107.1430] [INSPIRE].
R. Nakayama, The Holographic Fluid on the Sphere Dual to the Schwarzschild Black Hole, arXiv:1109.1185 [INSPIRE].
R.-G. Cai, L. Li, Z.-Y. Nie and Y.-L. Zhang, Holographic Forced Fluid Dynamics in Non-relativistic Limit, Nucl. Phys. B 864 (2012) 260 [arXiv:1202.4091] [INSPIRE].
R.-G. Cai, T.-J. Li, Y.-H. Qi and Y.-L. Zhang, Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term, Phys. Rev. D 86 (2012) 086008 [arXiv:1208.0658] [INSPIRE].
Y. Tian, X.-N. Wu and H.-b. Zhang, Poor man’s holography: how far can it go?, Class. Quant. Grav. 30 (2013) 125010 [arXiv:1204.2029] [INSPIRE].
V. Lysov and A. Strominger, From Petrov-Einstein to Navier-Stokes, arXiv:1104.5502 [INSPIRE].
T.-Z. Huang, Y. Ling, W.-J. Pan, Y. Tian and X.-N. Wu, From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime, JHEP 10 (2011) 079 [arXiv:1107.1464] [INSPIRE].
T.-Z. Huang, Y. Ling, W.-J. Pan, Y. Tian and X.-N. Wu, Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant, Phys. Rev. D 85 (2012) 123531 [arXiv:1111.1576] [INSPIRE].
C.-Y. Zhang, Y. Ling, C. Niu, Y. Tian and X.-N. Wu, Magnetohydrodynamics from gravity, Phys. Rev. D 86 (2012) 084043 [arXiv:1204.0959] [INSPIRE].
X. Wu, Y. Ling, Y. Tian and C. Zhang, Fluid/Gravity Correspondence for General Non-rotating Black Holes, Class. Quant. Grav. 30 (2013) 145012 [arXiv:1303.3736] [INSPIRE].
Y. Ling, C. Niu, Y. Tian, X.-N. Wu and W. Zhang, Note on the Petrov-like boundary condition at finite cutoff surface in gravity/fluid duality, Phys. Rev. D 90 (2014) 043525 [arXiv:1306.5633] [INSPIRE].
B. Wu and L. Zhao, Gravity-mediated holography in fluid dynamics, Nucl. Phys. B 874 (2013) 177 [arXiv:1303.4475] [INSPIRE].
B. Wu and L. Zhao, Holographic fluid from the nonminimally coupled scalartensor theory of gravity, Class. Quant. Grav. 31 (2014) 105018 [arXiv:1401.6487] [INSPIRE].
R.-G. Cai, Q. Yang and Y.-L. Zhang, Petrov type-I Spacetime and Dual Relativistic Fluids, Phys. Rev. D 90 (2014) 041901 [arXiv:1401.7792] [INSPIRE].
R.-G. Cai, Q. Yang and Y.-L. Zhang, Petrov type-I condition and Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity, JHEP 12 (2014) 147 [arXiv:1408.6488] [INSPIRE].
T. Moskalets and A. Nurmagambetov, Liouville mode in gauge/gravity duality, arXiv:1409.4186 [INSPIRE].
A. Coley, R. Milson, V. Pravda and A. Pravdova, Classification of the Weyl tensor in higher dimensions, Class. Quant. Grav. 21 (2004) L35 [gr-qc/0401008] [INSPIRE].
A. Coley, Classification of the Weyl Tensor in Higher Dimensions and Applications, Class. Quant. Grav. 25 (2008) 033001 [arXiv:0710.1598] [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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1412.8144
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hao, X., Wu, B. & Zhao, L. Flat space compressible fluid as holographic dual of black hole with curved horizon. J. High Energ. Phys. 2015, 30 (2015). https://doi.org/10.1007/JHEP02(2015)030
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)030