which involves long wavelength fluctuations around flat space in a Rindler patch the authors of [@Bredberg:2011jq; @Compere:2011dx] construct solutions to vacuum Einstein’s equations order by order in a perturbation expansion in gradients along the hypersurface directions. The resulting geometry has a regular Rindler horizon, and one obtains a regular solution to Einstein’s equations contingent on the fact that dynamics of the induced stress tensor on the hypersurface satisfies the incompressible Navier-Stokes equations.

While this development is fascinating, one is hampered from a first principles understanding of the physics from a holographic viewpoint, owing to the rather poorly understood concepts of flat space holography. Moreover, given the connection between fluid dynamics (albeit relativistic and conformal) and Einstein’s equations with negative cosmological constant as described by the aforementioned fluid/gravity correspondence [@Bhattacharyya:2008jc](and its non-relativistic extension in [@Bhattacharyya:2008kq] ), it is interesting to ask whether the construction in [@Bredberg:2011jq] can be obtained as a limit of the fluid/gravity map. If this is possible, one can then look for the field theoretic interpretation of the flat space problem.

Motivated by these issues, we consider a region of the AdS spacetime bounded by a timelike hypersurface $\Sigma_D$ at some radial position, say $r = r_D$ in 