Quantum Geometry and Black Holes

Understand

We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity.

• After an introduction that discusses the main conceptual issues we present some details about the classical and quantum geometry of isolated horizons and their quantum geometry and then use this scheme to give a natural definition of the entropy of black holes.
• The entropy computations can be neatly expressed in the form of combinatorial problems solvable with the help of methods based on number theory and the use of generating functions.
• The recovery of the Bekenstein-Hawking law and corrections to it is explained in some detail.