Holography and hydrodynamics: diffusion on stretched horizons

TL;DR

This paper demonstrates that horizon fluctuations in black-brane backgrounds display universal hydrodynamic behavior, with diffusion and shear modes characterized by simple formulas, supporting the holographic duality between gravity and quantum field theories.

Contribution

It provides explicit formulas for diffusion constants and shear viscosity from horizon metrics, confirming their universality and matching with independent AdS/CFT results for various branes.

Findings

Diffusive and shear modes are present in horizon fluctuations.

Diffusion constant and shear viscosity are given by simple metric formulas.

Shear viscosity to entropy density ratio equals /(4\u03c0) across examples.

Abstract

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\pi k_B), suggesting a special meaning of this value.