  Complementarity plays a pivotal role in understanding a diverse range of
quantum phenomena. Here, we show how the tradeoff between quantities of a
complete complementarity relation is modified in an arbitrary spacetime for a
particle with an internal spin. This effect stems from local Wigner rotations
in the spacetime, which couple the spin to the system's external degrees of
freedom. To conduct our study, we utilize two generalized delayed-choice
interferometers. Despite differences in complementarity tradeoffs inside the
interferometers, the interferometric visibility of both setups coincides in any
relativistic regime. Our results extend the finding that general relativity
induces a universal decoherence effect on quantum superpositions, as local
Wigner rotations, being purely kinematical, preclude any spin dynamics. To
illustrate, we analyze the Newtonian limit of our results.
