Built on

J. M. Ziman, “The General Variational Principle of Transport Theory,” Can. J. Phys. 34
1956
Earlier work this paper cites.
S. W. Hawking, “Black hole explosions,” Nature 248
1974
Earlier work this paper cites.
G. T. Horowitz and R. C. Myers, “The AdS / CFT correspondence and a new positive energy conjecture for general relativity,” Phys. Rev. D 59
1998
Earlier work this paper cites.
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
Earlier work this paper cites.
S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217
2001
Earlier work this paper cites.
D. T. Son and A. O. Starinets, “Minkowski space correlators in AdS / CFT correspondence: Recipe and applications,” JHEP 0209
2002
Earlier work this paper cites.
P. Kovtun, D. T. Son and A. O. Starinets, “Holography and hydrodynamics: Diffusion on stretched horizons,” JHEP 0310
2003
Earlier work this paper cites.
J. Zaanen, “Superconductivity: Why the temperature is high,” Nature, 430
2004
Earlier work this paper cites.
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
Earlier work this paper cites.
D. T. Son and A. O. Starinets, “Viscosity, Black Holes, and Quantum Field Theory,” Ann. Rev. Nucl. Part. Sci. 57
Original
2007
Earlier work this paper cites.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “The Viscosity Bound and Causality Violation,” Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP 0805
Original
2008
Earlier work this paper cites.
S. Kachru, X. Liu and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
Y. Kats and P. Petrov, “Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory,” JHEP 0901
Original
2009
Earlier work this paper cites.
A. Buchel, R. C. Myers and A. Sinha, “Beyond eta/s = 1/4 pi,” JHEP 0903
Original
2009
Earlier work this paper cites.
N. Iqbal and H. Liu, “Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm,” Phys. Rev. D 79
Original
2009
Earlier work this paper cites.
S. A. Hartnoll, “Lectures on holographic methods for condensed matter physics,” Class. Quant. Grav. 26
Original
2009
Earlier work this paper cites.

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2016

Entropy production, viscosity bounds and bumpy black holes

Hartnoll, Sean A., Ramirez, David M., Santos, Jorge E.

Understand

The ratio of shear viscosity to entropy density, $\eta/s$, is computed in various holographic geometries that break translation invariance (but are isotropic).

The shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain.
Fluctuations of the metric components $\delta g_{xy}$ are massive about these backgrounds, leading to $\eta/s < 1/(4\pi)$ at all finite temperatures (even in Einstein gravity).
As the temperature is taken to zero, different behaviors are possible.

Built on

J. M. Ziman, “The General Variational Principle of Transport Theory,” Can. J. Phys. 34
1956
Earlier work this paper cites.
S. W. Hawking, “Black hole explosions,” Nature 248
1974
Earlier work this paper cites.
G. T. Horowitz and R. C. Myers, “The AdS / CFT correspondence and a new positive energy conjecture for general relativity,” Phys. Rev. D 59
1998
Earlier work this paper cites.
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
Earlier work this paper cites.
S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217
2001
Earlier work this paper cites.
D. T. Son and A. O. Starinets, “Minkowski space correlators in AdS / CFT correspondence: Recipe and applications,” JHEP 0209
2002
Earlier work this paper cites.
P. Kovtun, D. T. Son and A. O. Starinets, “Holography and hydrodynamics: Diffusion on stretched horizons,” JHEP 0310
2003
Earlier work this paper cites.
J. Zaanen, “Superconductivity: Why the temperature is high,” Nature, 430
2004
Earlier work this paper cites.
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
Earlier work this paper cites.
D. T. Son and A. O. Starinets, “Viscosity, Black Holes, and Quantum Field Theory,” Ann. Rev. Nucl. Part. Sci. 57
Original
2007
Earlier work this paper cites.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “The Viscosity Bound and Causality Violation,” Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP 0805
Original
2008
Earlier work this paper cites.
S. Kachru, X. Liu and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev. D 78
Original
2008
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
Y. Kats and P. Petrov, “Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory,” JHEP 0901
Original
2009
Earlier work this paper cites.
A. Buchel, R. C. Myers and A. Sinha, “Beyond eta/s = 1/4 pi,” JHEP 0903
Original
2009
Earlier work this paper cites.
N. Iqbal and H. Liu, “Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm,” Phys. Rev. D 79
Original
2009
Earlier work this paper cites.
S. A. Hartnoll, “Lectures on holographic methods for condensed matter physics,” Class. Quant. Grav. 26
Original
2009
Earlier work this paper cites.