  The explicit expressions for the one-loop non-perturbative corrections to the
gravitational effective action induced by a scalar field on a stationary
gravitational background are obtained both at zero and finite temperatures. The
perturbative and non-perturbative contributions to the one-loop effective
action are explicitly separated. It is proved that, after a suitable
renormalization, the perturbative part of the effective action at zero
temperature can be expressed in a covariant form solely in terms of the metric
and its derivatives. This part coincides with the known large mass expansion of
the one-loop effective action. The non-perturbative part of the renormalized
one-loop effective action at zero temperature is proved to depend explicitly on
the Killing vector defining the vacuum state of quantum fields. This part
cannot be expressed in a covariant way through the metric and its derivatives
alone. The implications of this result for the structure and symmetries of the
effective action for gravity are discussed.
