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We construct the holographic dual of an electrically charged, localized defect in a conformal field theory at strong coupling, by applying a spatially dependent chemical potential. We find that the infrared 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.
Horowitz et al. (Thu,) studied this question.