Gravitationally induced neutrino oscillation phases in static spacetimes

We critically examine the recent claim of a ``new effect'' of gravitationally induced quantum mechanical phases in neutrino oscillations. Because this claim has generated some discussion in the literature we present here a straightforward calculation of the phase and clarify some of the conceptual issues involved, particularly in relation to the equivalence principle. When expressed in terms of the asymptotic energy of the neutrinos $E$ and Schwarzschild radial coordinates $r,$ the lowest order at which such a gravitational effect appears is $(GM\ensuremath{\Delta}{m}^{4}/\ensuremath{\Elzxh}{E}^{3})\mathrm{ln}{(r}_{B}{/r}_{A}).$

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