Destabilization of black holes and stars by generalized Proca fields

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.