Nonperturbative one-loop effective action for electrodynamics in curved space-time

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved space-time. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely to the gravitational correction.