Gravity-mediated holography in fluid dynamics

For any spherically symmetric black hole spacetime with an ideal fluid source, we establish a dual fluid system on a hypersurface near the black hole horizon. The dual fluid is incompressible and obeys Navier–Stokes equation subject to some external force. The force term in the fluid equation consists in two parts, one comes from the curvature of the hypersurface, the other comes from the stress-energy of the bulk fluid.