Spin entanglement and its monogamy relation in multi-event horizon spacetime

Abstract

We investigate the Hawking effect on quantum entanglement, considering the spin degree of freedom of the Dirac field in Schwarzschild-de Sitter (SdS) spacetime, which features both a black hole event horizon (BEH) and a cosmological event horizon (CEH). Our results show that both physically accessible and inaccessible spin entanglement are monotonic functions of the mass of the black hole, while inaccessible spin entanglement may be either monotonic or non-monotonic in relation to the cosmological constant. This behavior contrasts with the properties of spin entanglement in single-event horizon spacetime. From an information conservation perspective, the Hawking effect in multi-event horizon spacetime cannot arbitrarily redistribute spin entanglement. Therefore, we derive a monogamy relation that governs the redistribution of spin entanglement, indicating that quantum information in SdS spacetime is not lost but rather transformed between accessible and inaccessible forms.