In this lecture, we first considered entanglement across the horizon. By using techniques from Lecture 16, we derived the two point function for modes across the horizon. Modes across the horizon are independent degrees of freedom but they are nevertheless correlated in a specific manner if the horizon is smooth. We then turned to the simplest version of the information paradox. If Hawking radiation is universal with no knowledge of the initial state, then it appears that the final state at future null infinity is universal regardless of which initial state we started from. This appears to violate unitarity. This is not much of a paradox, as we see in Lecture 18. (Although we showed that remnants do not provide a resolution.)

Lecture 17 notes