In this paper we present the calculation of the production probability of an e − -e + pair in the presence of a strong, uniform and slowly rotating magnetic field by taking into account the presence of a weak background gravitational field. The gravitational field is treated perturbatively and it is shown how the curvature of the space-time metric induced by the gravitational field itself enhances the production probability with respect to the analogous one obtained in Minkowski space-time. (1) J (r) and V (1) J (r). Instead, the eigenstates U(1) J (r, t) and V (1) J (r, t) depend on time through the rotation operator Rx[ϑ(t)] = Rx(ωt).