  We study the helicity and chirality transitions of a high-energy neutrino
propagating in a Schwarzschild space-time background. Using both traditional
Schwarzschild and isotropic spherical co-ordinates, we derive an
ultrarelativistic approximation of the Dirac Hamiltonian to first-order in the
neutrino's rest mass, via a generalization of the Cini-Touschek transformation
that incorporates non-inertial frame effects due to the noncommutative nature
of the momentum states in curvilinear co-ordinates. Under general conditions,
we show that neutrino's helicity is not a constant of the motion in the
massless limit due to space-time curvature, while the chirality transition rate
still retains an overall dependence on mass. We show that the chirality
transition rate generally depends on the zeroth-order component of the
neutrino's helicity transition rate under the Cini-Touschek transformation. It
is also shown that the chiral current for high-energy neutrinos is altered by
corrections due to curvature and frame-dependent effects, but should have no
significant bearing on the chiral anomaly in curved space-time. We determine
the upper bound for helicity and chirality transitions near the event horizon
of a black hole. The special case of a weak-field approximation is also
considered, which includes the gravitational analogue of Berry's phase first
proposed by Cai and Papini. Finally, we propose a method for estimating the
absolute neutrino mass and the number of right-handed chiral states from the
expectation values of the helicity and chirality transition rates in the
weak-field limit.
