  We construct the holographic dual of an electrically charged, localised
defect in a conformal field theory at strong coupling, by applying a spatially
dependent chemical potential. We find that the IR behaviour of the spacetime
depends on the spatial falloff of the potential. Moreover, for sufficiently
localized defects with large amplitude, we find that a new gravitational
phenomenon occurs: a spherical extremal charged black hole nucleates in the
bulk: a hovering black hole. This is a second order quantum phase transition.
We construct this new phase with several profiles for the chemical potential
and study its properties. We find an apparently universal behaviour for the
entropy of the defect as a function of its amplitude. We comment on the
possible field theory implications of our results.
