Surface Layers in the Gravity/Hydrodynamics Correspondence

TL;DR

This paper reviews the AdS/hydrodynamics correspondence and investigates boundary layers between nonrelativistic flows, revealing discrepancies in the gravity dual's stress tensor due to derivative corrections in the flow velocity.

Contribution

It identifies the limitations of applying the correspondence to flow boundaries, highlighting the role of higher derivatives in the gravity dual's stress tensor.

Findings

Naive application yields a surface layer with stress tensor discrepancies.

Israel's matching conditions are not satisfied by the gravity dual in this context.

Derivative corrections to the flow velocity violate the thin wall approximation.

Abstract

I review the AdS/hydrodynamics correspondence, which provides a 1-1 map between large wavelength features of AdS black branes and conformal fluid flows. In this thesis I consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. I 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.