Ghost of vector fields in compact stars

Spontaneous scalarization is a mechanism that allows scalar field to go undetected in weak gravity environments and yet develop nontrivial configuration strongly gravitating systems. At the perturbative level it manifests as tachyonic instability around spacetimes solve Einstein's equations. The endpoint of this can significantly modify compact object's structure produce observational signatures field's presence. Does such exists for vector fields? Here we revisit model constitutes most straightforward generalization original perform analysis. We show ghost appears soon square naive effective mass squared becomes negative anywhere. This result poses serious obstacle generalizing spontaneous fields.