Gravitomagnetism and the Berry phase of photon in an rotating gravitational field

In this paper, we present an investigation of the Berry phase that a photon acquired during its propagating through a gravitational field produced by a Kerr black hole. Starting from the Maxwell equation in Kerr-Schild metric form of Kerr black hole, we give the zeroth order Hamiltonian of the photon under geometric optics approximation. The helicity state of the photon is then derived. We demonstrate that there are two factors leading to the Berry phase that the photon acquires in a gravitational field. These are the adiabatic transport of the local comoving tetrad and the rotation of the equivalent magnetic field that we introduce. The straightforward calculation show that the appearance of Berry phase is attributed to the twisted optical path due to the rotation of black hole. It is in fact analogous to the observed optical rotation for a linear polarized light propagating in an helical optical fiber.