The Surface Layers Dual to Hydrodynamic Boundaries

TL;DR

This paper investigates the gravity duals of hydrodynamic boundaries, revealing discrepancies in stress tensors due to derivative corrections that challenge existing matching conditions.

Contribution

It identifies the limitations of applying Israel's matching conditions to hydrodynamic boundaries in the AdS/hydrodynamics correspondence.

Findings

Naive boundary application yields a surface layer with stress tensor discrepancies.

Corrections from flow velocity derivatives violate Israel's finiteness assumption.

Neither stress tensor satisfies the null energy condition.

Abstract

The AdS/hydrodynamics correspondence provides a 1-1 map between large wavelength features of AdS black branes and conformal fluid flows. In this note we consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. We find that a naive application of the correspondence to these boundaries yields a surface layer in the gravity theory whose stress tensor is not equal to that given by the Israel matching conditions. In particular, while neither stress tensor satisfies the null energy condition and both have nonvanishing momentum, only Israel's tensor has stress. The disagreement arises entirely from corrections to the metric due to multiple derivatives of the flow velocity, which violate Israel's finiteness assumption in the thin wall limit.