https://doi.org/10.1140/epjc/s10052-021-09982-0
Regular Article - Theoretical Physics
Effects of gravitational lensing on neutrino oscillation in 
-spacetime
1
School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing, China
2
Department of Physics, Indian Institute of Technology Guwahati, 781039, Assam, India
3
Shanghai Astronomical Observatory, 80 Nandan Road, 200030, Shanghai, People’s Republic of China
4
Ulugh Beg Astronomical Institute, Astronomy St 33, 100052, Tashkent, Uzbekistan
5
National University of Uzbekistan, 100174, Tashkent, Uzbekistan
6
Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kori Niyoziy st., 100000, Tashkent, Uzbekistan
7
Department of Physics, Nazarbayev University, 53 Kabanbay Batyr Avenue, 010000, Astana, Kazakhstan
Received:
19
October
2021
Accepted:
30
December
2021
Published online:
10
January
2022
We study the effects of gravitational lensing on neutrino oscillations in the 
-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 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 and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.
© The Author(s) 2022
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