that there is a corresponding velocity field ${\hat u}^\mu$ (normalized with respect to the hypersurface metric) and a scalar function (the hypersurface temperature), which parameterize the stress tensor of the hypersurface, which not surprisingly takes the fluid dynamical form. The main novelty is that the stress tensor does not however correspond to that of a conformal fluid. The introduction of an explicit scale by way of the Dirichlet surface’s location engenders a non-vanishing trace, which curiously evolves in a highly suggestive manner under change of cut-off surface position, see .

Calling the totality of the data on the hypersurface ${\hat {\mathfrak X}}$ we further show that within the gradient expansion there is a one-to-one correspondence between the hypersurface data and the boundary data; $\varphi_D: {\mathfrak X} \to {\hat {\mathfrak  X}}$ is bijective. This then has the advantage that we can immediately understand the boundary dual of the bulk Dirichlet problem as a conformal fluid which is placed on a[^12] ‘dynamical background’ whose metric depends on the same set of variables that characterizes the fluid itself (in addition to the prescribed hypersurface metric). So from the boundary viewpoint there is a complete mixing between intrinsic and extrinsic data, which is the 