Effects of gravitational lensing on neutrino oscillation in $ \gamma $-spacetime

TL;DR

This paper investigates how gravitational lensing in $\gamma$-spacetime influences neutrino oscillations, revealing dependencies on neutrino masses, the deformation parameter $\gamma$, and extending analysis from two to three flavors.

Contribution

It introduces a detailed quantum-mechanical analysis of neutrino oscillations in $\gamma$-spacetime, including effects of lensing and deformation parameter, extending previous Schwarzschild results to more general scenarios.

Findings

Oscillation probability depends on absolute neutrino masses and the sign of mass squared difference.

The deformation parameter $\gamma$ significantly affects neutrino oscillations.

Results generalize known Schwarzschild spacetime outcomes to $\gamma$-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-flavor 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 flavors neutrino scenario and study the effects of the parameter $\gamma$ and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.