Kerr black holes as circular polarizers

TL;DR

This work analyzes spin-optics effects for light propagating near Kerr black holes, focusing on retrolensing and the second retrograde caustics. Using the Frolov–Shoom framework for Maxwell fields in curved spacetime, the authors compute polarization-dependent light trajectories and magnifications in extremal Kerr geometry, isolating retrograde contributions due to coordinate limitations for prograde paths. A key result is that the caustics split for different circular polarizations by up to $\sim 10^{-3}$ rad, corresponding to separations of order $10^{12}$ m at kilolight-year distances, suggesting that Earth-based observers could detect distinct circular polarizations depending on their location. This polarization-based signature provides a feasible observational handle on black hole spin in strong gravity, and the paper discusses strategies for identifying short-lived, polarized retrolensing signals from nearby or isolated black holes.

Abstract

We study the retrograde second caustics of extremal Kerr black holes, where the intensity of the light beam is infinitely magnified. We find that the caustics of different polarized beams are split by as much as $10^{-3}$rad by an external black hole for a suitable range of parameters. A lensing black hole at several lys away separates the polarized beams about $10^{12}$m apart. This splitting is larger than the radius of the Earth. Therefore, an observer on Earth would see different circularly polarized light according to their location. The polarization will change while the detector is wandering around. Thus, the polarization of light beams can be an important quantity in retrolensing observations.

Figures (8)

• Figure 1: A source emits non-polarized light. The unpolarized light is split into two polarized lights while passing a rotating black hole. Observers will see distinguishable polarization images based on their positions.
• Figure 2: The origin of the coordinate system is at the source. The x-direction, y-direction, and z-direction are parallel to $\hat{r}$, $\hat{\phi}$, and $\hat{\theta}$ respectively in the Boyer-Lindquist coordinate. The arrow on the black hole marks the z-direction in the Boyer-Lindquist coordinate.
• Figure 3: The secondary caustics on the celestial sphere: The light source is at radius $r=10^{10} M$, $\Phi_e=0$ and $y_e=0$. The spin parameter of the black hole is $a=-1$. The observer is at $r=10^9 M$. $\epsilon$'s are chosen accordingly. The gray vertical line marks the enlarged region shown in Fig.\ref{['y=0.1-enlarge']}.
• Figure 4: The secondary caustics on the celestial sphere: The light source is at radius $r=10^{10} M$, $\Phi_e=0$, and $y_e=0.1$. The spin parameter of the black hole is $a=-1$. The observer is at $r=10^9 M$. $\epsilon$'s are chosen accordingly. The gray vertical line marks $\Phi_o=5.5$ circle.
• Figure 5: The secondary caustics on the celestial sphere: The light source is at radius $r=10^{10} M$, $\Phi_e=0$ and $y_e=0$. The spin parameter of the black hole is $a=-1$. The observer is at $r=10^9 M$. $\epsilon$'s are chosen accordingly. The gray vertical line marks the enlarged region shown in Fig.\ref{['y=0-enlarge']}.