Surface Layers in the Gravity/Hydrodynamics Correspondence

Details Surface Layers in the Gravity/Hydrodynamics Correspondence Surface Layers in the Gravity/Hydrodynamics Correspondence

2010-11-18

arxiv.org/abs/1011.4254v1

Physics

High Energy Physics

High Energy Physics - Theory

139 pages, 5 eps figures, doctoral thesis Univ di Pisa (advisor Jarah Evslin)

Scientific paper

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.

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