Fluid/Gravity Correspondence For General Non-rotating Black Holes

In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier-Stocks equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier-Stocks system.