  A decade ago, it was shown that a wide class of scalar-tensor theories can
pass very restrictive weak field tests of gravity and yet exhibit
non-perturbative strong field deviations away from General Relativity. This
phenomenon was called `Spontaneous Scalarization' and causes the (Einstein
frame) scalar field inside a neutron star to rapidly become inhomogeneous once
the star's mass increases above some critical value. For a star whose mass is
below the threshold, the field is instead nearly uniform (a state which
minimises the star's energy) and the configuration is similar to the General
Relativity one. Here, we show that the spontaneous scalarization phenomenon is
linked to another strong field effect: a spontaneous violation of the weak
energy condition.
