Dirichlet problem for a scalar field propagating in using this linear problem to build intuition. In we pose the bulk Dirichlet problem for gravity in spacetime and solve it in the long wavelength approximation borrowing heavily on the results from the fluid/gravity correspondence. The remainder of the paper is then devoted to understanding the physics of our construction in various regimes: demonstrates how the Dirichlet surface dynamics, as governed by the conservation equation, arises from the boundary physics. Aided by this we argue that the Dirichlet dynamics is probably pathological past a critical radius and propose a non-relativistic scaling of the resulting fluid a la BMW in to cure this possible pathology. Finally, in we study the near-horizon Dirichlet problem and make contact with the recent work on the flat space Dirichlet problem (and its connection with Navier-Stokes equations). We end with a discussion in . Various appendices contain useful technical results. In particular, to aid the reader we provide a comprehensive glossary of our conventions and key formulae in . This is followed by a complete ‘Dirichlet dictionary’ relating hypersurface variables to boundary variables in for ready reference.

[*Note added:*]{} While this work being completed we received [@Kuperstein:2011fn] which 