  In this paper we analyze the action of the gravitational field on the
dynamical Casimir effect. We consider a massless scalar field confined in a
cuboid cavity placed in a gravitational field described by a static and
diagonal metric. With one of the plane mirrors of the cavity allowed to move,
we compute the average number of particles created inside the cavity by means
of the Bogoliubov coefficients computed through perturbative expansions. We
apply our result to the case of an oscillatory motion of the mirror, assuming a
weak gravitational field described by the Schwarzschild metric. The regime of
parametric amplification is analyzed in detail, demonstrating that our computed
result for the mean number of particles created agrees with specific associated
cases in the literature. Our results, obtained in the framework of the
perturbation theory, are restricted, under resonant conditions, to a short-time
limit.
