The holographic nature of null infinity! With Alok, Siddharth and Pushkal. https://arxiv.org/abs/2002.02448
I think that we have some exciting and interesting results. We clarify an important aspect of how holography should work in flat space — the question of how null infinity stores information about the bulk state. The answer seems to be that null infinity stores information more intricately than the AdS boundary. A small region near the past boundary of I^+ already has all information about massless excitations. But, as we go towards the future (on I^+) we may “lose” information. This means that a cut on I^+ always contains at least as much information as any cut to its future but not necessarily as much as a cut to its past. (The opposite is true on past null infinity.)
Its fun to explore what this means for the information paradox. Usually, people ask questions about how the information should “come out” of a black hole. But our results suggest that even in flat space, the information is always outside and so this is just the wrong question to ask. More specifically, this suggests that the von Neumann entropy of the state reduced on a segment on I^{+} doesn’t obey the Page curve but rather is trivially constant as one extends the segment to the future. Our results are not inconsistent with the recent discussions of the Page curve, where gravity it turned off at some point to obtain a factorized Hilbert space. But they do imply that those discussions are not immediately relevant for the evaporation of black holes in our world where gravity doesn’t suddenly get turned off.