Projective measurements and generation of entangled Dirac particles in Schwarzschild Spacetime

TL;DR

This paper investigates how projective measurements near a Schwarzschild black hole's event horizon can generate entangled Dirac particles, with entanglement affected by particle frequency and Hawking temperature.

Contribution

It demonstrates the creation of entangled particles via measurements near a black hole horizon and analyzes how entanglement varies with temperature and frequency.

Findings

Entanglement decreases with increasing particle frequency.

Entanglement increases with higher Hawking temperature.

Particles become maximally entangled as the black hole evaporates.

Abstract

It is shown that the projective measurements made by Bob who locates near the event horizon of the Schwarzschild black hole will create entangled particles detected by Alice who stays stationary at the asymptotically flat region. It is found that the degree of entanglement decreases as the frequency of the detected particles increases and approaches to zero as the frequency $\omega_\mathbf{k} \to\infty$. It is also noted that the degree of entanglement increases as the Hawking temperature increases. Especially, the particle state is unentangled when the Hawking temperature is zero and approaches a maximally entangled Bell state when the black hole evaporates completely.