  We show that the Aretakis instability of compact extremal horizons persists
in the planar case of interest to holography and discuss its connection with
the emergence of "semi-local quantum criticality" in the field theory dual. In
particular, the spatially localized power-law decay of this critical phase
corresponds to spatially localized power-law growth of stress-energy on the
horizon. For near-extremal black holes these phenomena occur transiently over
times of order the inverse temperature. The boundary critical phase is
characterized by an emergent temporal conformal symmetry, and the bulk
instability seems to be essential to preserving the symmetry in the presence of
interactions. We work primarily in the solvable example of charged scalar
perturbations of five-dimensional (near-)extremal planar Reissner-Nordstr\"om
anti-de Sitter spacetime and argue that the conclusions hold more generally.
