The CFT dual of the AdS Dirichlet problem

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.
This boundary fluid can be re-expressed as an emergent hypersurface
fluid which is non-conformal but has the same value of the shear
viscosity as the boundary fluid. The hypersurface dynamics arises as a
collective effect, wherein effects of the background are transmuted
into the fluid degrees of freedom. Furthermore, we demonstrate that
this collective fluid is forced to be non-relativistic below a
critical cut-off radius in AdS to avoid acausal sound propagation with
respect to the hypersurface metric. We further go on to show how one
can use this set-up to embed the recent constructions of flat
spacetime duals to non-relativistic fluid dynamics into the AdS/CFT
correspondence. (Reference : Based on arXiv:1106.2577)