Abstract
Abstract In this paper, we have investigated the mathematical components of the Dirac equation in curved space-time and how it can be applied to the analysis of neutrino oscillations. More specifically, we have developed a method for calculating the phase shift in flavor neutrino oscillations by utilizing a Taylor series expansion of the action, taking into account $\Delta m^4$ orders. In addition, we have used this method to assess how the phase difference in neutrino mass eigenstates changes due to the gravitational field described by the Johannsen spacetime.
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