Effects of gravitational lensing on neutrino oscillation in gamma -spacetime

Abstract

We study the effects of gravitational lensing on neutrino oscillations in the gamma -spacetime which describes a static, axially-symmetric and asymptotically flat solution of the Einstein’s field equations in vacuum. Using the quantum-mechanical treatment for relativistic neutrinos, we calculate the phase of neutrino oscillations in this spacetime by considering both radial and non-radial propagation. We show the dependence of the oscillation probability on the absolute neutrino masses, which in the two-flavour case also depends upon the sign of mass squared difference, in sharp contrast with the well-known results of vacuum oscillation in flat spacetime. We also show the effects of the deformation parameter gamma on neutrino oscillations and reproduce previously known results for the Schwarzschild metric. We then extend these to a more realistic three flavours neutrino scenario and study the effects of the parameter gamma and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.