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Previously it has been shown that imposing a Petrov-like boundary conditionon a hypersurface may reduce the Einstein equation to the incompressibleNavier-Stokes equation, but all these correspondences are established in thenear horizon limit. In this note, we remark that this strategy can be extendedto an arbitrary finite cutoff surface which is spatially flat, and theNavier-Stokes equation is obtained by employing a non-relativisticlong-wavelength limit.

The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality