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Correspondences between black holes and fluids have been discussed in twodifferent frameworks, the Fluid/Gravity correspondence and membrane paradigm.Recently, it has been discussed that these two theories can be understood asthe same theory if the cutoff surface is placed slightly outside the horizon.The bulk viscosity is different for these two theories, but it does notcontribute to physics since the fluid becomes incompressible in the nearhorizon limit. In the AdS/CFT correspondence, it is known that the fluidbecomes compressible and the bulk viscosity is zero, apart from the nearhorizon limit. In this paper, we consider the Fluid/Gravity correspondence inasymptotically non-AdS geometries. We put the cutoff surface near but at afinite distance from the horizon. Then, the model becomes the membrane paradigmwith compressible fluid. We show that the bulk viscosity is not negative atleast within the linear response regime. We also discuss the higher derivativecorrections in the stress-energy tensor.

Compressible Fluids in the Membrane Paradigm: non-AdS Fluid/Gravity correspondences