Electrogravitational conversion cross sections in static electromagnetic fields

We use Feynman perturbation techniques to analyze a classical process: the conversion of gravitational waves into electromagnetic waves (and vice versa) under the "catalytic" action of a static electromagnetic background field. Closed-form differential cross sections are presented for conversion in the Coulomb field of a point charge, electric and magnetic dipole fields, and uniform electrostatic and magnetostatic fields. Using the model calculation of conversion in a Coulomb field, we discuss the problems we must face when calculating non-gauge-invariant quantities, as is frequently done in literature. The cross sections are extremely small, but may lead to observable effects if allowed to act on astrophysical distance and time scales. The calculations also provide additional insight into the physics of electromagnetic detectors of gravitational waves.