Membrane Paradigm and Holographic Hydrodynamics

TL;DR

This paper explores how the membrane paradigm equations for black hole horizons can be reformulated as relativistic hydrodynamics equations, providing insights into the dual field theories via gauge/gravity duality.

Contribution

It demonstrates the recasting of membrane paradigm equations as relativistic conservation laws and derives transport coefficients for holographic dual field theories.

Findings

Membrane equations can be expressed as relativistic conservation laws.

Viscous transport coefficients are derived for dual field theories.

Entropy current form is obtained for holographic models.

Abstract

We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.