Gravitational analog of Faraday rotation in the magnetized Kerr and Reissner-Nordstr\"om spacetimes

TL;DR

This paper demonstrates that magnetic fields induce gravitational Faraday rotation and Stern-Gerlach effects in both Kerr and Reissner-Nordström spacetimes, even without rotation, with potential astrophysical implications for polarized light in strong gravity.

Contribution

It extends the understanding of gravitational Faraday rotation to nonrotating charged spacetimes immersed in magnetic fields, deriving exact expressions and highlighting the effects of magnetic fields on polarization rotation.

Findings

Magnetic fields cause gravitational Faraday rotation in nonrotating charged spacetimes.

Exact expressions for effects in magnetized Kerr and Reissner-Nordström spacetimes are derived.

Logarithmic corrections due to magnetic fields influence polarization rotation over distance.

Abstract

It is known that the gravitational analog of the Faraday rotation arises in the rotating spacetime due to the nonzero gravitomagnetic field. In this paper, we show that it also arises in the "nonrotating" Reissner-Nordstr\"om spacetime, if it is immersed in a uniform magnetic field. The non-zero angular momentum (due to the presence of electric charge and magnetic field) of the electromagnetic field acts as the twist potential to raise the gravitational Faraday rotation as well as the gravitational Stern-Gerlach effect in the said spacetimes. The twisting can still exist even if the mass of the spacetime vanishes. In other words, the massless charged particle(s) immersed in a uniform magnetic field are able to twist the spacetime in principle, and responsible for the rotation of the plane of polarization of light. This, in fact, could have applications in the basic physics and the analog models of gravity. Here, we also study the effect of magnetic fields in the Kerr and Reissner-Nordstr\"om spacetimes, and we derive the exact expressions for the gravitational Faraday rotation and the gravitational Stern-Gerlach effect in the magnetized Kerr and Reissner-Nordstr\"om spacetimes. Calculating the lowest order of the gravitational Faraday effect arisen due to the presence of a magnetic field, we show that the logarithm correction of the distance of the source and observer in the gravitational Faraday rotation and gravitational Stern-Gerlach effect for the said spacetimes is an important consequence of the presence of the magnetic field. From the astrophysical point of view, our result could be helpful to study the effects of (gravito)magnetic fields on the propagation of polarized photons in the strong gravity regime of the collapsed object.