Kerr black hole shadow from axion-photon coupling

We have investigated birefringence of photons in a Kerr black hole spacetime arising from axion-photon coupling and find that only the propagation of extraordinary rays depends on the coupling. We further study the shadow casted by the extraordinary lights and find that the axion-photon coupling yields a stretching or squeezing in the vertical direction. Such deformation becomes more heavy with the increasing black hole's spin parameter. The size of shadow slightly increases with the coupling strengthen. There also exists mirror symmetry between two shadows whose coupling parameters are opposite number each other in the non-rotating case, but the mirror symmetry gradually disappears with the increasing spin parameter. In the strong coupling case, there exist some self-similar fractal structures in the black hole shadow due to chaotic lensing. These features arising from axion-photon coupling could help us to understand deeply axion field and black hole shadows.