Causal hydrodynamics and the membrane paradigm

We obtain the relaxation time for the shear viscous stress for various geometries using the “membrane paradigm” formula proposed recently. We consider the generic Schwarzschild-AdS black holes (SAdS), the generic Dp-brane, the Klebanov-Tseytlin (KT) geometry, and the N=2* theory. The formula is the “shear mode” result and is not fully trustable, but it may be helpful to learn some generic behaviors about the relaxation time. For example, a simple formula summarizes all known results for SAdS, and a single expression summarizes the results for the Dp-brane and the KT geometry.