  Recently, a toy model was introduced to demonstrate that screening mechanisms
in alternative theories of gravitation can hide additional effects. In this
model a scalar field is charged under a $U(1)$ symmetry. In sufficiently
compact objects the scalar field spontaneously grows, i.e. the object
scalarizes, spontaneously breaking the $U(1)$ symmetry. Exactly as in the
$U(1)$ Higgs mechanism this leads to the emergence of a mass for the gauge
field.
  The aim of this paper is to provide an example of the physical consequences
if we consider this toy model as a prototype of Weak Equivalence Principle
(WEP) violations. We model neutron stars with a dipolar magnetic field to
compare the magnetic field behaviour of stars in Einstein-Maxwell theory on the
one hand and in scalar-tensor theory with the, so-called, gravitational Higgs
mechanism on the other hand.
