Electromagnetic Wave Generation and Propagation in Gravitational Fields

We use Feynman perturbation techniques to analyze some aspects of electromagnetic wave generation and propagation in weak gravitational fields. In the first part of this report we calculate differential cross sections dσ/dΩ for the scattering of plane electromagnetic waves by weakly gravitating and rotating bodies in the long-wavelength limit (wavelength of incident radiation >> radius of scatterer >> mass of scatterer). We find that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved), and that the two helicity states of the photon are scattered differently by a rotating body. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For the sake of comparison, we also compute the differential cross sections for the gravitational scattering of scalar and gravi­tational waves. For the latter there is neither helicity conservation nor helicity-dependent scattering; and the angular momentum has no polarizing effect on incident, unpolarized gravitational waves. In the second part of this report, we analyze 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 that we must face when calculating non-gauge­-invariant transition amplitudes, as is frequently done in the litera­ture. We conclude this report by pointing out how charged-particle beams may be used (in principle) as direction-sensitive gravitational­-wave detectors.