Electromagnetic phenomena induced by weak gravitational fields. Foundations for a possible gravitational wave detector

In the context of the weak-field approximation to the De Rham wave-vector equation, and applying the standard Lorentz gauge to both electromagnetism and gravitation, a linearized expression for the De Rham operator is derived. The derived equation is applied to solve (1) the interaction between plane, monochromatic, and polarized electromagnetic and gravitational waves and (2) the interaction between a transverse electric (${}_0{}^{}{}_{}{}^{}\mathrm{T}$ ${\mathrm{E}}_n$) mode, propagating in a rectangular wave guide, and a gravitational wave. The second result permits us to consider the possibility of a gravitational-wave antenna based on purely electromagnetic means, because new transverse electric and magnetic modes are generated, whose characteristics depend on the gravitational wave. Evidently this detector is completely different from that based on electromagnetic gravitational resonance designed by Braguinski and Manoukine. Also, in the optic limit of the De Rham equation the known expression for the equivalent index of refraction is obtained and other laws for the amplitude and polarization are derived.