Black holes are thermal objects which means the density matrix of the black hole is in a thermal state. This means that the black hole has to be maximally entangled with the rest of the universe to purify the state. So,
- at early times when very little radiation has left the black hole what (else) is it entangled with?
- we can always choose the infalling matter to be unentangled with anything else so what happens at the moment when the black hole forms that suddenly entangles it with it's surroundings and what does that say about the equivalence principle?
The notion of time used here is Kruskal-Szekeres time or any other nice foliation of the spacetime which are known to exist.