Abstract
The mass neutrino oscillation in the Kerr–Newman (K–N) spacetime is studied in the plane θ = θ0, and general equations of the 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 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 in the direction θ = 0. Finally, we calculate the proper oscillation length in the K–N spacetime. 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, a blue shift of the oscillation length takes place. We discuss the variation of the oscillation length influenced by the gravitational field strength, the rotation a2 and charge Q.
Highlights
Mass neutrino mixing and oscillations were proposed by Pontecorvo[1], and Mikheyev, Smirnov and Wolfenstein (MSW for short) explored the effect of transformation of one neutrino flavor into another in a medium with varying density[2, 3]
We extend the mass neutrino oscillation work from Schwarzschild spacetime to Kerr-Newman space-time, since the Kerr-Newman metric is rather important in black hole physics, where a most generally stationary solution with axial symmetry has been existing[51]
We have given the phase of mass neutrino propagating along the null and the time like geodesic in the gravitational field of a rotating symmetric and charged object, which is described by Kerr-Newman metric
Summary
Mass neutrino mixing and oscillations were proposed by Pontecorvo[1], and Mikheyev, Smirnov and Wolfenstein (MSW for short) explored the effect of transformation of one neutrino flavor into another in a medium with varying density[2, 3]. We give the general equations of the oscillation phases along the arbitrary null and the time-like geodesics, respectively, in the equal θ plane, θ = θ0. We calculate the oscillation phases along the geodesics with L = 0 in the equatorial plane This kind of geodesics is important in K-N space-time. In the Schwarzschild space-time with non-rotating spherically symmetry, particles with L = 0 can propagate along the radial geodesics. The decrease in the local energy leads to the decrease in the oscillation length as the neutrino travels out of the gravitational field. The rotation a2 of the gravitational field shortens the oscillation length in other equal θ plane, compared with the length in R-N space time. In Sec., we give the general expressions of the oscillation phases along the null and time-like geodesics in arbitrary equal θ = θ0 plane.
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