Curved space-time corrections to Faraday rotation in magnetized plasmas far from Schwarzschild black holes

Context. In this manuscript, we analyze the effect of Schwarzschild space-time curvature on the Faraday rotation of quasi-monochromatic circularly polarized electromagnetic waves. Aims. We show how the plane of polarization of the electromagnetic waves is rotated, retaining information about the source of space-time curvature and the plasma properties around it. Methods. We investigate right-handed and left-handed circularly polarized electromagnetic waves propagating in this space-time along a radial magnetic field in a multicomponent plasma. The coupling between the plasma and the gravitational field produces corrections to the Faraday rotation proportional to the ratio of the black hole's Schwarzschild radius to the (far) distance to it, the plasma frequency, and the inverse of the wave's frequency. Results. In general, the rotation angle provides information about the plasma properties, the external magnetic field, and the Schwarzschild black hole mass. Hence, we propose that Faraday rotation can be used to obtain information not only about magnetized plasma but also about static astrophysical compact objects that curve space-time.