  Nonminimally coupled free scalar fields may be unstable in the spacetime of
compact objects. Such instability can be triggered by classical seeds or, more
simply, by quantum fluctuations giving rise to the so-called {\em vacuum
awakening effect}. Here, we investigate how the parameter space which
characterizes the instability is affected when the object gains some rotation.
For this purpose, we focus on the stability analysis of nonminimally coupled
scalar fields in the spacetime of slowly spinning matter shells.
