Effects of Hawking radiation and Wigner rotation on fermion entanglement

Abstract

In this work, we report that the Hawking radiation effect on fermions is fundamentally different from the case of scalar particles. Intrinsic properties of fermions (exclusion principle and spin) affect strongly the interaction of fermions with both Hawking radiation and metric of the spacetime. In particular we have found the following: first, while the fermion vacuum state seen by the Rindler observer is an entangled state in which the right and left Rindler wedge states appear in correlated pairs as in the case of the scalar particles, the entanglement disappears in the excited state due to the exclusion principle; second, the spin of the fermion experiences the Winger rotation under a uniform acceleration; and third, the quantum information of fermions encoded in spin (entangled state is composed of different spin states but with the same mode function) is dissipated not by the Hawking radiation but by the Wigner rotation as the pair approaches the event horizon.