Quantum nonlocality phenomena in scalar and Dirac fields near a Schwarzschild black hole

Abstract

In this work, we explore the impact of the Hawking effect on quantum nonlocality, specifically the maximum violation of the Bell-CHSH inequality, for both scalar and Dirac fields within Schwarzschild spacetime. We reveal the nuanced behavior of the Bell-CHSH inequality as the Hawking temperature (HT) varies. For scalar fields, we observe distinct degradation patterns in the Bell-CHSH inequality, influenced by the state parameter α and its normalized counterpart 1 − α 2 . In contrast, Dirac fields exhibit two distinct degradation trajectories, each converging to different nonzero minimum values as HT approaches infinity T → ∞ , however, this does not apply to the maximally entangled state. Remarkably, the maximum violation of Bell-CHSH inequality becomes zero for scalar fields at infinite HT, while it stabilizes at a finite nonzero value for Dirac fields. Additionally, the quantum nonlocality robustness of the Dirac fields is stronger than that of the scalar fields. Therefore, this study enhances our understanding of the dynamic characteristics of nonlocality within scalar and Dirac fields near a Schwarzschild black hole.