Observables for the Effect of Gravity on Electromagnetic Polarization

Abstract: Does gravity affect the polarization of electromagnetic radiation in an observable way? The effect of gravity on the observed polarization of a ray of electromagnetic radiation is investigated for an arbitrary 4-dimensional spacetime and radiation with a frequency spectrum within the geometric optics limit and with arbitrary state of polarization. Focusing on effects observable by a single inertial observer, we show how the presence of curvature along the null geodesic of polarized electromagnetic radiation may induce observable changes in the state of polarization. We find a set of scalars that quantify the effect and derive their transport equations. Two of these scalars, the polarization degree and the circular polarization degree, are polarization state observables that are conserved along the radiation geodesic. Four observables that quantify time rate of change of the observed state of polarization are identified. These observables and their corresponding transport equations provide a complete representation of how gravity affects the observed state of polarization of electromagnetic radiation with frequencies above the geometric optics limit. Polarization wiggling is sourced by curvature twist, which is a scalar derived from the Riemann tensor. Curvature twist is closely related to the magnetic part of the Weyl tensor, the second Weyl scalar as well as the rotation of the rest frame geodesic congruence. The results of this paper are valid for any metric theory of gravity.