Non-Relativistic Fluid Dual to Asymptotically AdS Gravity at Finite Cutoff Surface

TL;DR

This paper explores the duality between non-relativistic fluids and asymptotically AdS gravity at a finite cutoff surface, deriving fluid dynamics equations and viscosity properties in Einstein and Gauss-Bonnet gravity.

Contribution

It provides a detailed analysis of dual fluid behavior at finite cutoff surfaces, including viscosity ratios and Navier-Stokes equations, extending holographic fluid duality to finite regions.

Findings

Viscosity to entropy density ratio remains constant with cutoff surface.

Derived incompressible Navier-Stokes equations for dual fluids.

Established non-running of shear viscosity ratio in both gravity theories.

Abstract

Using the non-relativistic hydrodynamic expansion, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to the second order of the expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy ensity of dual fluid does not run with the cutoff surface. The incompressible Navier-Stokes equations are also obtained in both cases.