Neutrino oscillations in Kerr-Newman space-time

The mass neutrino oscillation in Kerr-Newman(K-N) space-time is studied in the plane $\theta=\theta_{0}$, and the general equations of oscillation phases are given. The effect of the rotation and electric charge on the phase is presented. Then, we consider three special cases: (1) The neutrinos travel along the geodesics with the angular momentum $L=aE$ in the equatorial plane. (2) The neutrinos travel along the geodesics with L=0 in the equatorial plane. (3) The neutrinos travel along the radial geodesics at the direction $\theta=0$. At last, we calculate the proper oscillation length in the K-N space time. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. When the neutrino travels out of the gravitational field, the blue shift of the oscillation length takes place. We discussed the variation of the oscillation length influenced by the gravitational field strength, the rotation $a^{2}$ and charge $Q$.