  We demonstrate that black holes and stars in general relativity can be
destabilized by perturbations of non-minimally coupled vector fields. Focusing
on static and spherically symmetric backgrounds, our analysis shows that black
holes with sufficiently small mass and stars with sufficiently high densities
are subject to ghost or gradient-type instabilities. This holds for a large
class of vector-tensor theories whenever non-minimal couplings contribute to
linearized dynamics about a state with vanishing vector field and applies to
generalized Proca models that have sparked attention for their potential role
in cosmology and astrophysics. The stability criteria translate into bounds of
relevance for low-scale theories of dark energy and for ultra-light dark matter
scenarios.
