  In this paper we will present very recent results obtained in the ambit of
quantum electrodynamics in curved spacetime. We utilize a newly developed
non-perturbative heat kernel asymptotic expansion on homogeneous Abelian
bundles over Riemannian manifolds in order to compute the one-loop effective
action for scalar and spinor fields in curved spacetime under the influence of
a strong covariantly constant electromagnetic field. In this framework we
derived, in particular, the gravitational corrections, up to linear terms in
Riemannian curvature, to Schwinger's result for the creation of particles in a
strong electric field.
