Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field

Understand

We present firstly the equation of motion for the photon coupled to a special bumblebee vector field in a Kerr black hole spacetime and find that the propagation of light depends on its polarization due to the birefringence phenomenon.

• The dependence of black hole shadow on the light's polarization is dominated by the rotation of black hole.
• In the non-rotating case, we find that the black hole shadow is independent of the polarization of light.
• However, the status is changed in the rotating case, in which the black hole shadow depends on the light's polarization and the coupling between bumblebee vector field and electromagnetic field.