Black hole entropy calculations based on symmetries

Symmetry-based approaches to the black hole entropy problem have a number of attractive features; in particular, they are very general and do not depend on the details of the quantization method. However, we point out that, of the two available approaches, one faces conceptual problems (also emphasized by others), while the second contains certain technical flaws. We correct these errors and, within the new, improved scheme, calculate the entropy of three-dimensional black holes. We find that, while the new symmetry vector fields are well defined on the `stretched horizon', and lead to well defined Hamiltonians satisfying the expected Lie algebra, they fail to admit a well defined limit to the horizon. This suggests that, although the formal calculation can be carried out at the classical level, its real, conceptual origin probably lies in the quantum theory.