Black Holes and Entropy in Loop Quantum Gravity

Black holes in equilibrium and the counting of their entropy within Loop Quantum Gravity are reviewed. In particular, we focus on the conceptual setting of the formalism, briefly summarizing the main results of the classical formalism and its quantization. We then focus on recent results for small, Planck scale, black holes, where new structures have been shown to arise, in particular an effective 'quantization' of the entropy. We discuss recent results that employ in a very effective manner results from number theory, providing a complete solution to the counting of black hole entropy. We end with some comments on other approaches that are motivated by loop quantum gravity.