  This paper claims that local space-time curvature can non-trivially
contribute to the properties of orbital angular momentum in quantum mechanics.
Of key importance is the demonstration that an extended orbital angular
momentum operator due to gravitation can identify the existence of orbital
states with half-integer projection quantum numbers "m" along the axis of
quantization, while still preserving integer-valued orbital quantum numbers "l"
for a simply connected topology. The consequences of this possibility are
explored in depth, noting that the half-integer "m" states vanish as required
when the locally curved space-time reduces to flat space-time, fully recovering
all established properties of orbital angular momentum in this limit. In
particular, it is shown that a minimum orbital number of "l = 2" is necessary
for the gravitational interaction to appear within this context, in perfect
correspondence with the spin-2 nature of linearized general relativity.
