Constraints on the quantum state of pairs produced by semiclassical black holes

Abstract

The pair-production process for a black hole (BH) is discussed within the framework of a recently proposed semiclassical model of BH evaporation. Our emphasis is on how the requirements of unitary evolution and strong subadditivity act to constrain the state of the produced pairs and their entanglement with the already emitted BH radiation. We find that the state of the produced pairs is indeed strongly constrained but that the semiclassical model is consistent with all requirements. We are led to the following picture: Initially, the pairs are produced in a state of nearly maximal entanglement amongst the partners, with a parametrically small entanglement between each positive-energy partner and the outgoing radiation, similar to Hawking's model. But, as the BH evaporation progresses past the Page time, each positive-energy partner has a stronger entanglement with the outgoing radiation and, consequently, is less strongly entangled with its negative-energy partner. We present some evidence that this pattern of entanglement does not require non-local interactions, only EPR-like non-local correlations.