Causal hydrodynamics and the membrane paradigm
Makoto Natsuume
TL;DR
This paper calculates the shear viscous stress relaxation time in various holographic geometries using the membrane paradigm, revealing simplified formulas that capture generic behaviors across different models.
Contribution
It derives a unified approach to estimate relaxation times in diverse geometries via the membrane paradigm, providing simple formulas for complex holographic models.
Findings
Unified formulas for relaxation times in SAdS, Dp-brane, and KT geometries
Identification of generic behaviors in shear viscous relaxation
Potential insights into hydrodynamic properties of holographic theories
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-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.
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