  Near horizon geometries have been widely studied, and have found many
applications. Certain static, near horizon geometries are now understood to be
bulk duals to CFTs with static scale-invariant sources under the AdS/CFT
correspondence. However, static near-horizon geometries aren't just
scale-invariant, they have extra `enhanced' symmetry. This means that they can
only be the bulk duals for a special class of static, scale-invariant sources
that share this enhanced symmetry. The purpose of this paper is to consider
bulk duals for more generic static, scale-invariant sources, without this extra
symmetry. These solutions are quite different to near-horizon geometries. In
place of the extremal horizon they have a null singularity. We find specific
examples of such bulk geometries numerically for the cases of pure gravity, and
for an abelian gauge field.
