I will review some older results on counting states and calculating the entropy of isolated horizons in loop quantum gravity in the presence of charges/matter fields on the horizon. One question that I will answer at least partially in some examples is if the matter DOF contribute to the entropy, and if so, to what order.
I will also briefly touch on some newer results and work in progress...
In this talk I will show that edge modes in free Maxwell theory in 3+1 dimensions lead to correlated fluctuations in the large gauge charges of a subregion and its complement, and result in a non-trivial contribution to the entanglement entropy across a cut of future null infinity. I will then outline a generalization of these ideas to gravity. In particular, I will highlight a novel relation...
Einstein field equations are not conformally invariant. Despite this fact, conformal geometry plays an important role in description of asymptotics of the solutions via Penrose conformal compactification. Moreover, in many cases such conformal compactification of solution is smooth. It turns out that these facts are linked to a fundamental object in conformal geometry, Fefferman-Graham...
