A vacuum density matrix for asymptotically flat gravity

I will review the recent progress in understanding the vacua of asymptotically flat gravity, and in particular highlight the fact that the vacuum is not unique as was originally assumed, but rather infinitely degenerate. This allows us to construct a nontrivial density matrix associated to the vacuum, which can be fixed by using known infrared properties of perturbative gravity. Finally, I will compute the mean and variance of the entanglement entropy, showing that both quantities are in fact proportional to the area.