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-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.

17 pages, 10 figures. Comments welcome. This version is accepted for publication at EPJC

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• A class of Taub-NUT-scalar metrics via Ehlers transformations
• A class of charged-Taub-NUT-scalar metrics via Harison and Ehlers Transformations
• Periodic orbits and their gravitational wave radiations in $\gamma$-metric
• The neutrino flavor oscillations in the static and spherically symmetric black-hole-like wormholes
• Effects of bumblebee gravity on neutrino motion
• Gravitational effects on neutrino decoherence in Lense-Thirring metric
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