  It has been shown that gravitational fields produced by realistic
classical-matter distributions can force quantum vacuum fluctuations of some
nonminimally coupled free scalar fields to undergo a phase of exponential
growth. The consequences of this unstable phase to the background spacetime
have not been addressed so far due to known difficulties concerning
backreaction in semiclassical gravity. It seems reasonable to believe, however,
that the quantum fluctuations will "classicalize" when they become large
enough, after which backreaction can be treated in the general-relativistic
context. Here we investigate the emergence of a classical regime out of the
quantum field evolution during the unstable phase. By studying the appearance
of classical correlations and loss of quantum coherence, we show that by the
time backreaction becomes important the system already behaves classically.
Consequently, the gravity-induced instability leads naturally to initial
conditions for the eventual classical description of the backreaction. Our
results give support to previous analyses which treat classically the
instability of scalar fields in the spacetime of relativistic stars, regardless
whether the instability is triggered by classical or quantum perturbations.
