Wilsonian Approach to Fluid/Gravity Duality

Understand

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered.

• Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed.
• For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface.
• A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived.