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 complete, 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 quantum gravity is a non-perturbative formulation which is background independent, two properties which are essential 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, providing 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. 1 General relativity General relativity successfully describes the gravitational field, in terms of space-time geometry, on large scales. However on small scales it is hardly being probed by direct observations. Nevertheless, there are indirect indications, and all of them point to its failure: singularity theorems imply not only infinite densities but even a complete breakdown of evolution after a finite amount of proper time for most realistic solutions [1]. The best known examples are cosmological situations and black holes. Plenary talk at “Einstein’s Legacy in the New Millenium,” Puri, India, December 2005 e-mail address: [email protected]