Abstract
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--anti-de Sitter black holes (SAdS), the generic $\mathrm{D}p$-brane, the Klebanov-Tseytlin (KT) geometry, and the $\mathcal{N}={2}^{*}$ 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 $\mathrm{D}p$-brane and the KT geometry.
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