  We consider in the framework of the fluid/gravity correspondence the dynamics
of hypersurfaces located in the holographic radial direction at r = r_0. 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 in arXiv:1103.1657
via the null horizon dynamics.
