  Quantum fields in compact stars can be amplified due to a semiclassical
instability. This generic feature of scalar fields coupled to curvature may
affect the birth and the equilibrium structure of relativistic stars. We point
out that the semiclassical instability has a classical counterpart, which
occurs exactly in the same region of the parameter space. For negative values
of the coupling parameter the instability is equivalent to the well-known
"spontaneous scalarization" effect: the plausible end-state of the instability
is a static, asymptotically flat equilibrium configuration with nonzero
expectation value for the quantum fields, which is compatible with experiments
in the weak-field regime and energetically favored over stellar solutions in
general relativity. For positive values of the coupling parameter the new
configurations are energetically disfavored, and the end-point of the
instability remains an open and interesting issue. The vacuum instability may
provide a natural mechanism to produce spontaneous scalarization, leading to
new experimental opportunities to probe the nature of vacuum energy via
astrophysical observations of compact stars.
