Non-relativistic fluid dual to asymptotically AdS gravity at finite cutoff surface

摘要: Using the non-relativistic hydrodynamic limit, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to second order of the non-relativistic hydrodynamic expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy density of dual fluid does not run with the cutoff surface. The incompressible Navier-Stokes equations are also obtained in both cases.