An analysis of the optical and electromagnetic properties of gravitational fields in general relativity



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From first principles of electromagnetism, a formalism analogous to that of classical optics is developed for an analysis of stationary metric fields as optical media. In the geometric approximation, stationary metrics are shown to generate Fresnel surfaces without centers of inversion; it is shown that no material free gravitational field can display birefringence, nor can it generate a "forced birefringence," of a relativistic nature, in isotropic material introduced into the field. For the ray path, the Frenet triad, the curvature and the torsion are all calculated both for an arbitrary weak field and a spatially isotropic strong field; also, at the same approximation level, the equation for the deflection of the ray path is given for the above two metric classes. At the next level of approximation, the transport equation for the vector fields is presented. This equation demonstrates that a "polarization rotation" exists for certain metric fields. A corresponding equation is developed from a purely geometric analysis of a curve on a surface. Since the question is in dispute, concerning whether or not a rotation of the polarization plane takes place for light propagating between infinite limits past a rotating spherical body, this system is studied as a practical example. The finding here is in the negative; however, a small postive effect is found for light originating on or in the vicinity of the surface of the body. This finding helps resolve the conflicting results obtained by G. V. Skrotskii and J. Piebanski. The present work, by an independent method, has obtained a result which agrees with Plebanski