Compressible fluids in the membrane paradigm: Non-AdS fluid/gravity correspondences

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