Complete complementarity relations in curved spacetimes

TL;DR

This paper extends the concept of complete complementarity relations to curved spacetimes, analyzing how quantum properties like entanglement evolve for particles in Schwarzschild spacetime, revealing oscillations between different quantum states.

Contribution

It introduces a method to apply complementarity relations in curved spacetime using local Lorentz transformations, linking quantum properties along a particle's world line.

Findings

Spin states oscillate between separable and entangled in geodetic orbits.

Oscillation frequency increases as orbit approaches Schwarzschild radius.

Complementarity relations remain valid in curved spacetime.

Abstract

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 study 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 non-geodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit gets nearer to the Schwarzschild radius $r_s$.