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 nonminimally 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 Einstein-Proca theories with nonminimal couplings, including 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 ultralight dark matter scenarios.

Figure 1

Region plot of the GP parameters for which a destabilization of the RN BH occurs, blue for $G_6$ and orange for $G_{4,X}/{\mu }^2$ (normalized by the Schwarzschild radius).

Figure 2

Critical values of the GP parameters for which an instability is triggered in stars modeled by uniform density (“UDS”) and $\gamma =5/3$ polytropic index (“Poly”) as inferred from Eq. (11). Colored points label different values of the central pressure, ranging from ${10}^{-2}$ (red; upper-right end) to ${10}^4$ (blue; lower end) in arbitrary units such that $K=1$ (the constant appearing in the polytropic EOS). Despite this arbitrariness, the comparison between different pressures and between the two stellar models is meaningful.