Scattering of circularly polarized light by a rotating black hole

TL;DR

This paper investigates how the polarization of light affects its scattering, bending, and timing when passing near a rotating black hole, using a modified geometric optics approximation to include polarization effects.

Contribution

It introduces a first-order polarization-dependent correction to photon trajectories in Kerr spacetime, extending geometric optics to account for polarization effects in black hole scattering.

Findings

Photon bending angle varies with polarization.

Image position depends on photon polarization.

Photon arrival times are polarization-dependent.

Abstract

We study scattering of polarized light by a rotating (Kerr) black hole of the mass M and the angular momentum J. In order to keep trace of the polarization dependence of photon trajectories one can use the following dimensionless parameter: $\varepsilon=\pm (\omega M)^{-1}$, where $\omega$ is the photon frequency and the sign + (-) corresponds to the right (left) circular polarization. We assume that $|\varepsilonl << 1$ and use the modified geometric optics approximation developed in [1], that is we include the first order in $\varepsilon$ polarization dependent terms into the eikonal equation. These corrections modify late time behavior of photons. We demonstrate that the photon moves along a null curve, which in the limit $\varepsilon=0$ becomes a null geodesic. We focus on the scattering problem for polarized light. Namely, we consider the following problems: (i) How does the photon bending angle depend on its polarization; (ii) How does position of the image of a point-like source depend on its polarization; (iii) How does the arrival time of photons depend on their polarization. We perform the numerical calculations that illustrate these effects for an extremely rotating black hole and discuss their possible applications.