  We study the dynamical stability of Proca-Higgs stars, in spherical symmetry.
These are solutions of the Einstein-Proca-Higgs model, which features a
Higgs-like field coupled to a Proca field, both of which minimally coupled to
the gravitational field. The corresponding stars can be regarded as Proca stars
with self-interactions, while avoiding the hyperbolicity issues of
self-interacting Einstein-Proca models. We report that these configurations are
stable near the Proca limit in the candidate stable branches, but exhibit
instabilities in certain parts of the parameter space, even in the candidate
stable branches, regaining their stability for very strong self-interactions.
This shows that for these models, unlike various examples of scalar boson
stars, self-interactions can deteriorate, rather than improve, the dynamical
robustness of bosonic stars.
