QUANTUM GEOMETRY AND ITS IMPLICATIONS FOR BLACK HOLES∗

General relativity successfully describes space–times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time, there have been indications that quantum gravity will provide a more com-plete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quan-tum gravity is a non-perturbative formulation which is background independent, two properties which are essentially close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings, one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, provid-ing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another