Lecture 16: Entropy at null infinity
In this lecture, we examined the von Neumann entropy of a segment (-\infty, u_0) of scri-plus in a theory of gravity. We showed that if one considers the fine-grained entropy, then the principle of holography of information tells us that this entropy is a constant, independent of u_0. This formalizes the statement that "information is always outside" in a theory of gravity.
We discussed the physics of this claim and contrasted black holes with ordinary objects, like burning coal.
We also discussed why these results were consistent with the Page curve that has recently been computed in AdS/CFT. In obtaining the Page curve, one couples a holographic system to a nongravitational bath. The entire system has a nongravitational description. One can then ask a well-defined question about how one part of this nongravitational system is entangled with its complement. It is this entanglement entropy that follows a Page curve. In this setup, the gravitational dual is used only as a calculational tool to answer a nongravitational question.
