Using Hamilton-Jacobi Equation to Study the Neutrino Oscillations in the Stationary Space-Time

We study the mass neutrino oscillation by solving Hamilton-Jacobi equation in the Kerr-Newman-Kasuya space-time, as an important example of the stationary space-time, and give the general expression of the oscillation phase. A special case, the geodesic with L=aE is considered. Then, the proper oscillation length is studied carefully. The effects of the gravitational field, the rotating parameter a, the electric charge and magnetic charge on the oscillation length are given. It is worth noting that a blue shift of the oscillation length rather than a red shift takes place as the neutrino travels out of the gravitational field.