Title: Replica wormholes and the entropy of Hawking radiation
Abstract: I will review recent work on applying ideas of holography to the problem of evaporating black holes. I will consider a model of a black hole coupled to holographic matter that can be thought of as living on a Randall-Sundrum brane on the boundary of a higher dimensional AdS space. I will show how the standard RT formula in the higher dimensions reproduces the Page curve indicative of unitary black hole evaporation. These results suggest a new prescription for computing the entanglement entropy of the Hawking radiation whereby new contributions from the interior of the black hole, or what we call ''islands'', become relevant. I will show how the island conjecture can be derived more generally from replica wormholes which are saddles of the Euclidean gravitational path integral connecting the different replica sheets.