On the Quantum Information Content of a Hawking Pair

We introduce a new probe designed to keep track of the quantum information content of a Hawking pair as a function of the distance from the black hole horizon. We compute the entropy content of this Hawking pair probe via a semi-classical replica method that relies on free field Wick contractions and their leading order gravitational back reaction on the black hole horizon area. We find that the information transfer from the black hole state to the Hawking pair is triggered by a geometric transition that, somewhat surprisingly, takes place at a macroscopic distance from the horizon. We relate our computation to recent insights about the role of von Neumann algebras in holography.