About the Incompleteness of the Semiclassical Picture in the BH-Information Paradox and the Quantum Hair emerging from the Coupling of Quantum Matter and Quantum Space-Time Degrees of Freedom

We argue that the semiclassical analysis of the black hole information paradox is incomplete and has to be completed by an explicit entanglement of matter and quantum gravity degrees of freedom. We study in detail the evaporation process from beginning to end in the light of our extension and show that a pure initial state remains pure over the full evaporation process, including the final state which remains after the black hole has completely evaporated. By the same token we show how the quantum hair is encoded in the micro structure of the (final) gravitational state which is entangled with the (final) radiation state.