CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces

Understand

We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation.

• We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface.
• Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime.
• On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a `dynamical' background metric which depends on the local fluid velocities and temperature.