Electromagnetic Field and Wave Propagation in Gravitation

Abstract

From the physical three-vector Maxwell equations for an electromagnetic (E.M.) field in static gravitation, we examine the artifice of replacing the gravitation by an equivalent medium and we find modified Debye potentials for an E.M. wave in a simple, angularly homogeneous, material medium in a Schwarzs-child gravitational field. The fact that these potentials do not obey the generalized scalar wave equation implies that gravitation scatters the vector E.M. wave and a scalar wave differently. Also, we obtain and solve by perturbation the amplitude and eikonal equations for a high-frequency wave in a weak spherical gravitational field. To the order M/r, the state of transverse polarization does not change along a ray path whereas the transverse-field amplitudes are modified by the factor e^(M/r) which strengthens the field near the mass. The longitudinal-field amplitude, on the other hand, is modified by e^(−M/r). These effects, in principle, may provide a further test of classical E.M. theory and general relativity.