Gravitational Lensing and Oscillations of Neutrinos in Yukawa Black Hole Spacetime

We study gravitational lensing of neutrinos and the resulting flavor-oscillation probabilities in a Yukawa black hole spacetime, which introduces a Yukawa-type correction to the standard metric. Employing the plane-wave formalism in curved spacetime together with the weak-field approximation, we derive analytically the ν_e → ν_μ transition probability P_eμ^lens for the two distinct lensed paths and evaluate it numerically for astrophysically motivated parameters. The Yukawa correction enters the oscillation phase through three computable integrals and manifests as a systematic shift of oscillation peaks toward smaller azimuthal angles with increasing charge parameter, while leaving the oscillation amplitude essentially unchanged. The lens mass dominates the oscillation frequency: increasing the mass from 1.5 M⊙ to 9.0 M⊙ at a fixed charge raises the number of visible peaks in a given interval by a factor of approximately six. Furthermore, the normal mass hierarchy consistently yields peak transition amplitudes of P_eμ ≈ 0.75, substantially larger than those observed for the inverted hierarchy.

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