Holographic screens and transport coefficients in the fluid-gravity correspondence

We consider in the framework of the fluid-gravity correspondence the dynamics of hypersurfaces located in the holographic radial direction at r=r₀. We prove that these hypersurfaces evolve, to all orders in the derivative expansion and including all higher curvature corrections, according to the same hydrodynamics equations with identical transport coefficients. The analysis is carried out for normal fluids as well as for superfluids. Consequently, this proves the exactness of the bulk viscosity formula derived by us via the null horizon dynamics.