Entanglement Entropy in Black Hole microstates

We review the thermodynamic behaviour and paradoxes arising from a classical description of Black Holes. Then we interpret them as solutions of Supergravity, seen as the low effective energy of Superstring Theory. This enables for a correct count of the microstates responsible for the entropy of the black hole, and suggests a resolution of the black hole issues: the Fuzzball Prosal. The prototypical example of a supersymmetric black hole with finite horizon area is the D1-D5-P black hole in five dimensions. Some of the microstates contributing to the entropy of this black hole have been identified as fuzzballs, presenting as regular horizonless geometries. To test the holographic dictionary between states and geometries we will compute holographically the entanglement entropy of an interval in a sub-class of these states, using the Ryu-Takayanagi prescription.