The spooky ghost of vectorization

An interesting mechanism for the formation of hairy black holes occurs when a vector field, non-minimally coupled to a source term, grows from a perturbation of the vacuum black hole, aka vectorization. Its study has, however, been lacking, in part due to the constant threat of ghost instabilities that have plagued vector fields. In this work, we show evidence that, in a generic family of extended-vector-tensor theories where the vector field is non-minimally coupled to the model's invariant (source term), a spherically symmetric vectorized black hole always suffers from ghost instabilities. These ultimately turn the process of vectorization astrophysically unviable.