Phase evolution of the photon in Kerr spacetime

In this paper, we explore some aspects of the gravitational lens effects due to a Kerr black hole. Under the eikonal approximation of the Maxwell equations in curved space, the spin function of a photon in the degenerate metric is determined. Furthermore, we present an investigation of the phase factor that a photon acquires in Kerr spacetime. The resulting phase consists of two parts: a real and an imaginary one. The real part has been interpreted as contributing a rotational angle of the plane polarization for linearly polarized light, and the imaginary one results in the light intensity amplification along with the photon's trajectory in the gravitational field. Finally, we provide the so-called "Sagnac factor" related to the phase shift.