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The explicit expressions for the one-loop non-perturbative corrections to thegravitational effective action induced by a scalar field on a stationarygravitational background are obtained both at zero and finite temperatures. Theperturbative and non-perturbative contributions to the one-loop effectiveaction are explicitly separated. It is proved that, after a suitablerenormalization, the perturbative part of the effective action at zerotemperature can be expressed in a covariant form solely in terms of the metricand its derivatives. This part coincides with the known large mass expansion ofthe one-loop effective action. The non-perturbative part of the renormalizedone-loop effective action at zero temperature is proved to depend explicitly onthe Killing vector defining the vacuum state of quantum fields. This partcannot be expressed in a covariant way through the metric and its derivativesalone. The implications of this result for the structure and symmetries of theeffective action for gravity are discussed.

the journal of high energy physics/the journal of high energy physics

Non-perturbative corrections to the one-loop free energy induced by a  massive scalar field on a stationary slowly varying in space gravitational  background