  This paper investigates the properties of spin-1/2 particle Zitterbewegung in
the presence of a general curved space-time background described in terms of
Fermi normal co-ordinates, where the spatial part is expressed using general
curvilinear co-ordinates. Adopting the approach first introduced by Barut and
Bracken for Zitterbewegung in the local rest frame of the particle, it is shown
that non-trivial gravitational contributions to the relative position and
momentum operators appear due to the coupling of Zitterbewegung frequency terms
with the Ricci curvature tensor in the Fermi frame, indicating a formal
violation of the weak equivalence principle. Explicit expressions for these
contributions are shown for the case of quasi-circular orbital motion of a
spin-1/2 particle in a Vaidya background. Formal expressions also appear for
the time-derivative of the Pauli-Lubanski vector due to space-time curvature
effects coupled to the Zitterbewegung frequency. As well, the choice of
curvilinear co-ordinates results in non-inertial contributions in the time
evolution of the canonical momentum for the spin-1/2 particle, where
Zitterbewegung effects lead to stability considerations for its propagation,
based on the Floquet theory of differential equations.
