Kerr black holes as circular polarizers

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 $$10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> 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 $$10^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> </mml:math> 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.