Holography and hydrodynamics: Diffusion on stretched horizons

By P. Kovtun, D. Son, A. Starinets. 2003

718 citations recorded by the source corpus.

We show that long-time, long-distance fluctuations of plane-symmetric horizons exhibit universal hydrodynamic behavior. By considering classical fluctuations around black-brane backgrounds, we find both diffusive and shear modes. The diffusion constant and the shear viscosity are given by simple formulas, in terms of metric components. For a given metric, the answers can be interpreted as corresponding kinetic coefficients in the holographically dual theory. For the near-extremal Dp, M2 and M5 branes, the computed kinetic coefficients coincide with the results of independent AdS/CFT calculations. In all the examples, the ratio of shear viscosity to entropy density is equal to hbar/(4? kB), suggesting a special meaning of this value.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8ed41e21c048efa12b36eb859f8a1bd29c797812

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Citations in the corpus

Brownian Motion in AdS/CFT (2008, neutral): “previously in [45,46,47,48] and more recently in [49] where there is a nice discussion regarding the dynamics of the stretched horizon and the universality of hydrodynamic coefficients.”
Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT (2008, neutral): “Contents”
Entropy current in conformal hydrodynamics (2008, background): “A non-exhaustive list of references include [1, 2, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35] .”
AdS/CFT Duality User Guide (2014, background): “l relativity such as metric, curvature, and the Einstein equation as a prerequisite. But, for completeness, we will review them in Chap. 2. If this is not enough, read textbooks of general relativity [10, 11, 12] (e.g., ﬁrst 8 chapters of [10]). References [10, 11] are elementary textbooks (but Ref.”
Lecture notes on Generalised Hydrodynamics (2019, background): “Modern perspectives have shown how its basic principles can be extended or deepened to account for many of the sometimes exotic systems that are of current interest in high-energy and condensed matter physics [6, 7, 8, 9, 10, 11, 12, 13].”
Gauge-gravity duality and thermalization of a boost-invariant perfect fluid (2006, background): “On a theoretical ground, a comment is in order about the well-known calculation of the viscosity to entropy ratio [10] in the static BH configuration.”
Hydrodynamics of R-charged black holes (2006, background): “The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to 1/4π.”
On string theory duals of Lifshitz-like fixed points (2009, background): “we can find that the universal bound for the shear viscosity η to the entropy density s ratio [27] is saturated for the current case: η s = 1 4π .”
Holographic Hydrodynamics with a Chemical Potential (2009, background): “Hence if c1 is positive, both of these contributions lead to a violation of the conjectured KSS bound [15].”
Universal hydrodynamics of non-conformal branes (2009, background): “However, once we allow the temperature in the definition of b in (4.2) and uµ to become z-dependent, ds2 = dρ2 4ρ2fb(z)(ρ) + [ηµν + (1− fb(z)(ρ))uµ(z)uν(z)]dzµdzν ρ , (4.4) we have to correct the metric (4.4) at each order in the derivative expansion to still fulfill the equations of motions.”