  The spin-orbit interaction (SOI) of light has been intensively studied in
nanophotonics because it enables sensitive control of photons' spin degree of
freedom and thereby the trajectory of the photons, which is useful for
applications such as signal encoding and routing. A recent study showed that
the SOI of photons manifests in the presence of a gradient in the permittivity
of the medium through which the photons propagate; this enhances the scattering
of circularly polarized light and results in the photons propagating along
twisted trajectories. Here we theoretically predict that, because of the
equivalence between an inhomogeneous dielectric medium and a gravitational
field demonstrated in transformation optics, a significant SOI is induced onto
circularly polarized light passing by the gravitational lens of a black hole.
This leads to: i) the photons to propagate along chiral trajectories if the
size of the blackhole is smaller than the wavelength of the incident photons,
ii) the resulting image of the gravitational lens to manifest an azimuthal
rotation because of these chiral trajectories. The findings open for a way to
probe for and discover subwavelength-size black holes using circularly
polarized light.
