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Abstract

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