Complete complementarity relations in curved spacetimes

We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we investigate the behavior of these different complementary properties of massive spin-1/2 particles in the Schwarzschild spacetime. For geodetic circular orbits, we find that the spin state of one particle oscillates between a separable and an entangled state. For nongeodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit nears the Schwarzschild radius r(s).

Automated summary

The study indicates that in curved spacetimes, complementarity aspects are connected as the quanton travels through its world line. Specifically in the Schwarzschild spacetime, the behavior of complementary properties of massive spin-1/2 particles varies with different types of orbits.