The black hole information puzzle can be solved if two conditions are met: information about what falls inside a black hole must remain encoded in d.o.f that persist after the black hole has completely evaporated. Moreover, these d.o.f must not contribute significantly to the energy of the system, given that the macroscopic mass of the initial black hole has been radiated to infinity in the form of Hawking radiation. The presence of Planckian geometric d.o.f provides a natural mechanism for achieving these two conditions. In this talk, I will illustrate both key aspects of this mechanism using a solvable toy model of a quantum black hole. I'll start by showing that near the singularity, a massless scalar field in a Kantowski Sachs spacetime is a good approximation to an Hawking particle of zero angular momentum falling into a black hole, and to its backreaction. I'll then show how the quantization of the total system, in a way inspired by loop quantum gravity, naturally brings in Planckian geometric d.o.f. The quantum dynamics thus obtained is totally solvable and allows us to show how matter interacts with these Planckian d.o.f. Finally, I'll explain how correlations between the outgoing Hawking radiation and the ingoing one dissipate in favor of correlations with the Planckian geometric d.o.f. The latter therefore seem necessary to restore the purity of the outgoing Hawking radiation.
Jacopo Mazza
