Liouville mode in Gauge/Gravity Duality

Understand

We establish solutions corresponding to AdS4 static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature.

• Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations.
• We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry.
• We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range.